text:
Existence of solution to parabolic equations with mixed boundary condition on non-cylindrical domain

Existence of solution to parabolic equations with mixed boundary condition on non-cylindrical domain

Tujin Kim111The author’s research was supported by TWAS, UNESCO and AMSS in Chinese Academy of Sciences. Daomin Cao 222Supported by Chinese Science Fund for Creative Research Group(10721101) Institute of Mathematics, Academy of Sciences, Pyongyang, Democratic People’s Republic of Korea33footnotemark: 3 Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, P. R. China
Abstract

In this paper we are concerned with the initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains in spatial-temporal space. We obtain the existence of a weak solution to the problem. In the case of the linear equation the parts for every type of boundary condition are any open subsets of the boundary being nonempty the part for Dirichlet condition at any time. Due to this it is difficult to reduce the problem to one on a cylindrical domain by diffeomorphism of the domain. By a transformation of unknown function and penalty method we connect the problem to a monotone operator equation for functions defined on the non-cylindrical domain. In this way a semilinear problem is considered when the part of boundary for Dirichlet condition is cylindrical.

keywords:
Parabolic equation, Non-cylindrical domain, Mixed boundary condition, Existence
MSC: 35K20, 35K55, 35A15

1 Introduction

There are vast literature for parabolic differential equations on non-cylindrical domain and various methods have been used to study them. In bhl () the energy inequality for a linear equation with homogeneous Dirichlet boundary condition is proved, thus unique existence of solution is studied. For domains expanded along time existence and uniqueness of solution to initial boundary value problem of the linear(cf. e (), ku () and kp ()), semilinear(cf. krr ()) and nonlinear(cf. ku ()) equations with homogeneous Dirichlet boundary condition are studied. For such domains and boundary conditions krr () also deals with attractor; and bps () considers unique existence of solution to a linear Schrödinger-type equation. In bg () dealing with the Dirichlet problem, they assume only Hölder continuity on time-regularity of the boundary. In ls () semigroup theory is improved and the obtained result is applied to the initial boundary value problem of a linear parabolic equation with inhomogeneous Dirichlet condition on non-cylindrical domain. There are some literatures for unique existence of initial boundary value problems of linear equations relying on the method of potentials (see c () and references therein). Domains in l1 () and l2 (), where existence, uniqueness and regularity are studied, are more general, that is, ”initial” condition is given on a hypersurface in spatial-temporal space instead of the plane . In lms1 () optimal regularity of solution to a special kind of 1-dimensional problem is considered. Neumann problem of heat equations (cf. hl ()), parabolic equation with Robin type boundary condition (cf. ks ()) in non-cylindrical domains and behavior of solutions to the initial-boundary value problems of nonlinear equations (cf. k () and t ()) are studied. In lcm () and mlm () optimal control and controllability of parabolic equation with homogenous Dirichlet condition on non cylindrical domain, respectively are studied.

Also, there are many literatures for the initial boundary value problems with mixed boundary conditions.
Under certain assumptions the non-cylindrical domains are transformed to a cylindrical one. The initial boundary value problems of linear parabolic equations with mixed time dependent lateral boundary condition on cylindrical domains are studied (cf. bfo1 (), bfo2 (), sa ()). The boundary conditions on the lateral surfaces in bfo1 () may be either two of the following classical ones: Dirichlet, Neumann and Robin, but one part for a kind of boundary condition is a connected and relatively open subset of the lateral surface and the boundary of the part is tangent to the plane . In bfo2 () the first part is concerned with a classical problem on cylindrical domains and the result is applied to the problem with zero initial condition and lateral mixed boundary conditions on a cylindrical domain, where the non-cylindrical surface for boundary condition is transformed to a cylindrical one by a diffeomorphism. The lateral boundary surface of the cylindrical domain in bfo2 () is also divided into two parts, and one part for a kind of boundary condition is connected and relatively open subset of the boundary surface and at each point is transverse to the hyperplane . Developing a method in abstract evolution equations, sa () is concerned with linear parabolic problems on cylindrical domains with mixed variable inhomogeneous Dirichlet and Neumann conditions. But, here change along time of distance of the sections of part of boundary for Dirichlet condition must be dominated by a Lipschitz continuous function in time . In sa () as application of the result, unique existence of solution to a linear parabolic problem with homogeneous Dirichlet boundary condition on non-cylindrical domains is considered.

Section 4 in l3 () deals with the linear parabolic problem on non-cylindrical domain with Robin and Dirichlet boundary conditions, where the surface for Dirichlet condition is cylindrical type. lvw () and lwv () study existence, uniqueness and regularity of solutions to the initial boundary value problems of linear and semilinear parabolic equations on non-cylindrical domains, which is related to the the combustion phenomena. The domains in lvw () and lwv () are bordered with a part of cylindrical type surface where homogeneous Neumann condition is given, non-cylindrical hypersurfaces where Dirichlet boundary one is given and planes . Thus, by change of spatial independent variable they transform the problems to classical problems on cylindrical domains where Dirichlet and Neumann conditions, respectively, are given on cylindrical surfaces. In lt () some differential inclusions are studied and the result is applied to the following problem

 ut−Δu∈F(u)inΩ,−∂∂nu∈β(u)onγ,
 u=0onΓ−γ,u(x,0)=ξinΩ0,

where is a non-cylindrical domain in spatial-temporal space, is its lateral surface, is a part of a cylindrical surface, and is a proper lower semicontinuous convex function from to with .

On the other hand, in s () a time-dependent Navier-Stokes problem on a non-cylindrical domain with a mixed boundary condition is considered. In s () the part of boundary where homogeneous Dirichlet condition is given is cylindrical type and the boundary condition on the other part of boundary is such a special one that guarantee existence of solution to an elliptic operator equation obtained by penalty method.

In this paper we are concerned with linear and semilinear parabolic equations on non-cylindrical domains with mixed boundary conditions which may include inhomogeneous Dirichlet, Neumann and Robin conditions together. In the case of linear equation the parts for every type of boundary condition are any open subsets of the boundary being nonempty the part for Dirichlet condition at any time. This rises difficulty in reducing the problem to one on cylindrical domains in bfo1 (), bfo2 () and sa () or one in lvw (), lwv (), l3 () and lt ().

Our idea is to use a transformation of unknown function by which the problem is connected to a monotone operator equation for functions defined on the non-cylindrical domain. In this way we can also consider semilinear equation when the part of boundary for Dirichlet condition is cylindrical.

This paper is composed of 5 sections. In Section 2 notation, the problem, the definition of weak solution and the main result are stated. In Section 3 by a change of unknown function an equivalent problem is derived. Section 4 is devoted to an auxiliary penalized problem. In Section 5 the proof of the main result is completed.

2 Problem and main result

Let be bounded connected domains of and be open subsets of such that and . Let be outward normal unit vector on the boundary and be outward normal unit vector on for fixed .
Let and . Let .

For function defined on define by

 β(y)=(∫T0∥y∥2Ω(t)dt)12

whenever the integral make sense. Let

 D(Q)={φ:φ∈C∞(¯Q),φ|Σ0=0},V(Q)={the completion of D(Q) under the normβ(y)},W(Q)={the completion of D(Q) in the spaceH1(Q)}

and be duality product between and . By the condition , is a norm in .

We use the following

Assumption 2.1

The hypersurface belongs to for and to for and for any there exist a diffeomorphisms on in the class which maps onto , and is in for , where is the unit operator.

Remark 2.1

Let and be any functions such that and Jacobian , where and . Then , where satisfies Assumption 2.1.

We are concerned with the following initial boundary value problem

 ∂y∂t−N∑i,j=1∂∂xi(aij(x,t)∂y∂xj)+N∑i=1bi(x,t)∂y∂xi+c(x,t,y)=g(x,t), (2.1)
 y|Σ0=¯y|Σ0,(k(x,t)y+N∑i,j=1aij(x,t)ni∂y∂xj)∣∣Σ1=f(x,t), (2.2)
 y(x,0)=y0(x)∈L2(Ω(0)), (2.3)

where and are functions satisfying the following conditions

is Lipschitz continuous with respect to uniformly for  and measurable with respect to for fixed and and

Remark 2.2

On a part of where we have Neumann condition.

When , in view of (2.2) we have

 ∫Q∂y∂tudxdt =(y(x,T),u(x,T))Ω(T)−(y0,u(x,0))Ω(0) (2.4) +∫Σ1yucos(^ν,t)dσ−∫Qy∂u∂tdxdt,
 −∫QN∑i,j=1∂∂xi(aij(x,t)∂y∂xj)udxdt =N∑i,j=1∫Qaij(x,t)∂y∂xj∂u∂xidxdt (2.5) +∫Σ1k(x,t)yudσ−∫Σ1f(x,t)udσ,

where is the angle between and the positive direction of -axis. Also, if , then (cf. Lemma 2.2, ch. 2 in ggz ()).

In view of (2.4) and (2.5), we introduce the following

Definition 2.1

A function is called a solution to (2.1)-(2.3) if satisfies the following

 y−¯y∈V(Q), −∫Qy∂v∂tdxdt+N∑i,j=1∫Qaij(x,t)∂y∂xj∂v∂xidxdt+N∑i=1∫Qbi(x,t)∂y∂xivdxdt +∫Qc(x,t,y)vdxdt+∫Σ1[yvcos(^ν,t)+k(x,t)yv]dσ =(y0,v(x,0))Ω(0)+∫Qg(x,t)vdxdt+∫Σ1f(x,t)vdσ ∀v∈W(Q)withv(x,T)=0.

Our main result of this paper is the following

Theorem 2.1

Suppose that conditions hold and that either is linear with respect to or and is invariant under the diffeomorphism in Assumption 2.1. Then there exists a solution to problem (2.1)-(2.3) provided that is valid.

3 Transformation of unknown function

For the sake of simplicity, we will use the same constants in the estimates unless confusion will be caused.

It is known that there exists a function such that

 ψ(x)>0∀x∈Ω(0),ψ|∂Ω(0)=0% and|∇ψ|>0∀x∈¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯Ω(0)∖ω0,

where (cf. Lemma 1.1 in cik ()).

Lemma 3.1

There exists a function such that

 φ(x,t)>0onQ,φ(x,t)=0onΣand−∂φ(x,t)∂n>η>0onΣ,

where is the space of functions which are twice continuously differentiable with respect to and continuously differentiable with respect to on .

Proof Take , where is the diffeomorphism from onto , which is the inverse of the one given in Assumption 2.1. Then the conclusion follows from the properties of function and Assumption 2.1.

Let us make a change by

 u=ek1t+k2φ(x,t)y, (3.1)

where and are constants to be determined later. Let and (2.2) is satisfied. Then,

 ek1t+k2φ(x,t)∂y∂t=∂u∂t−(k1+k2∂φ∂t)u, −ek1t+k2φ(x,t)N∑i,j=1∂∂xi(aij(x,t)∂y∂xj)= −N∑i,j=1∂∂xi(aij∂u∂xj)+2∑ijaijk2∂φ∂xj∂u∂xi +k2u[∑ij∂aij∂xi∂φ∂xj−k2∑ijaij∂φ∂xi∂φ∂xj+∑ijaij∂2φ∂xi∂xj], ek1t+k2φ(x,t)N∑i=1bi(x,t)∂y∂xi=N∑i=1[bi(x,t)∂u∂xi−bi(x,t)k2∂φ∂xiu].

Also, we have that

 N∑i,j=1aij(x,t)ni∂u∂xj∣∣Σ1= =(N∑i,j=1aij(x,t)ni∂y∂xjek1t+k2φ(x,t)+N∑i,j=1aij(x,t)nik2∂φ(x,t)∂xju)∣∣Σ1 =(N∑i,j=1aij(x,t)ni∂y∂xjek1t+k2φ(x,t)+k2∂φ(x,t)∂nN∑i,j=1aij(x,t)ninju)∣∣Σ1 =(f(x,t)ek1t−k(x,t)u+k2∂φ(x,t)∂nN∑i,j=1aij(x,t)ninju)∣∣Σ1

where the fact that and its corollary have been used.

Taking into account these facts, we have

 ∂u∂t−N∑i,j=1∂∂xi(aij(x,t)∂u∂xj)+N∑i=1Bi(x,t)∂u∂xi+C(x,t,u)=G(x,t), (3.2)
 u|Σ0=¯u|Σ0,(K(x,t)u+N∑i,j=1aij(x,t)ni∂u∂xj)∣∣Σ1=F(x,t), (3.3)
 u(x,0)=u0≡y0(x)ek2φ(x,0)∈L2(Ω(0)), (3.4)

where

 Bi(x,t)=bi(x,t)+2∑jaijk2∂φ∂xj, (3.5) C(x,t,u)=ek1t+k2φ(x,t)c(x,t,e−k1t−k2φ(x,t)u)−(k1+k2∂φ∂t)u +k2u[∑ij∂aij∂xi∂φ∂xj−k2∑ijaij∂φ∂xi∂φ∂xj+∑ijaij∂2φ∂xi∂xj−∑ibi∂φ∂xi], G(x,t)=ek1t+k2φ(x,t)g, F(x,t)=ek1tf, ¯u=ek1t+k2φ(x,t)¯y,

and

 K(x,t)=k(x,t)−k2∂φ∂n∑i,jaijninj. (3.6)

Now, we take

which is possible by Lemma 3.1 and . Functions and , respectively, satisfy the conditions for and in and .

Lemma 3.2

In the sense of Definition 2.1 existence of solution to problems (2.1)-(2.3) and (3.2)-(3.4) are equivalent

Proof First, let us prove that if is a solution in the sense of Definition 2.1 to problem (2.1)-(2.3), then is a solution in the sense of Definition 2.1 to problem (3.2)-(3.4).

For , put . Then

 −∫Qy∂v∂tdxdt=−∫Que−k1t−k2φ∂ek1t+k2φ¯v∂tdxdt =−∫Qu∂¯v∂tdxdt−∫Q(k1+k2∂φ∂t)uvdxdt, N∑i,j=1∫Qaij(x,t)∂y∂xj∂v∂xidxdt= =N∑i,j=1∫Qaij(x,t)∂(e−k1t−k2φu)∂xj∂(ek1t+k2φ¯v)∂xidxdt =N∑i,j=1∫Qaij[∂u∂xje−k1t−k2φ−uk2e−k1−k2φ∂φ∂xj]× ×[ek1t+k2φ∂¯v∂xi+ek1t+k2φk2∂φ∂xi¯v]dxdt =N∑i,j=1∫Qaij[∂u∂xj∂¯v∂xi+k2∂φ∂xi∂u∂xj¯v−k22∂φ∂xj∂φ∂xiu¯v−k2∂φ∂xju∂¯v∂xi]dxdt≡I.

Integrating by parts in the last term above, we have

 I =N∑i,j=1∫Qaij(x,t)∂y∂xj∂v∂xidxdt=N∑i,j=1∫Qaij∂u∂xj∂¯v∂xidxdt +N∑i,j=1∫Q2k2aij∂φ∂xi∂u∂xj¯vdxdt−∫Σ1aijk2∂φ∂nninju¯vdσ +N∑i,j=1∫Qk2[∂aij∂xi∂φ∂xju¯v−k2aij∂φ∂xj∂φ∂xiu¯v+aij∂2φ∂xi∂xju¯v]dxdt.

Also,

 ∑i∫Qbi∂y∂xivdxdt=∑i∫Qbi∂u∂xi¯vdxdt−∑i∫Qbik2∂φ∂xiu¯vdxdt, ∫Qc(x,t,y)vdxdt=∫Qc(x,t,e−k1−k2φu)ek1t+k2φ¯vdxdt.

The facts and are equivalent, and so from above we can see that is a solution to (3.2)-(3.4) in the sense of Definition 2.1. In the same way we can see that if is a solution to problem (3.2)-(3.4) in the sense of Definition 2.1, then is a solution in the sense of Definition 2.1 to (2.1)-(2.3).

Therefore, in what follows we will consider the existence of a solution to problem (3.2)-(3.4). To this end, in the next section we will consider an auxiliary problem.

4 An auxiliary problem

The main purpose in this section is to find a function satisfying the following

 um−¯u∈W(Q), (4.1) ∫Q1m∂um∂t∂v∂tdxdt−∫Qum∂v∂tdxdt+∫QN∑i,j=1aij(x,t)∂um∂xj∂v∂xidxdt +∫QN∑i=1Bi(x,t)∂um∂xivdxdt+∫QC(x,t,um)vdxdt +∫Σ1[umvcos(^ν,t)+K(x,t)umv]dσ+(um(x,T),v(x,T))Ω(T) =(u0,v(x,0))Ω(0)+∫QG(x,t)vdxdt+∫Σ1F(x,t)vdσ ∀v∈W(Q),

where are positive integers.

We have the following result.

Theorem 4.1

Let in (3.1) be as (3.7). Then, for some in (3.1), which is taken before (4.7), there exists a unique solution to problem (4.1).

Proof Set , define an operator and an element , respectively, by

 ∀w,v∈W(Q); ⟨Amw,v⟩=∫Q1m∂u∂t∂v∂tdxdt−∫Qu∂v∂tdxdt+N∑i,j=1∫Qaij(x,t)∂u∂xj∂v∂xidxdt +N∑i=1∫QBi(x,t)∂u∂xivdxdt+∫QC(x,t,u)vdxdt +∫Σ1[uvcos(^ν,t)+K(x,t)uv]dσ+(u(x,T),v(x,T))Ω(T)

and

 ⟨L,v⟩=(u0,v(x,0))Ω(0)+∫QG(x,t)vdxdt+∫Σ1F(x,t)vdσ.

Now, let us consider problem of finding such that

 Amw=L. (4.2)

By the conditions and , operator is Lipschitz continuous. For any letting , we have that

 ⟨Amw1−Amw2,w⟩= (4.3) ∫Q1m∂w∂t∂w∂tdxdt−∫Qw∂w∂tdxdt+N∑i,j=1∫Qaij(x,t)∂w∂xj∂w∂xidxdt +N∑i=1∫QBi(x,t)∂w∂xiwdxdt+∫Q[C(x,t,w1+¯u)−C(x,t,w2+¯u)]wdxdt

On the other hand, by integrating by parts we get

 −∫Qw∂w∂tdxdt=12[|w(0)|2Ω(0)−|w(T)|2Ω(T)−∫Σ1w2cos(^ν,t)dσ]. (4.4)

From (4.3) and (4.4) we conclude that for any

 ⟨Amw1−Amw2,w⟩=∫Q1m∂w∂t∂w∂tdxdt+∫QN∑i,j=1aij(x,t)∂w∂xj∂w∂xidxdt (4.5) +∫QN∑i=1Bi(x,t)∂w∂xiwdxdt+∫Q[C(x,t,w1+¯u)−C(x,t,w2+¯u)]wdxdt +∫Σ1[12w2cos(^ν,t)+K(x,t)w2]dσ+12|w(0)|2Ω(0)+12|w(x,T)|2Ω(T).

It follows from (3.6) and the choice of mentioned above that

 ∫Σ1[12w2cos(^ν,t)+K(x,t)w2]dσ≥0. (4.6)

Note that in (3.5) and in (3.6) are independent of . Therefore, taking in the expression of in (3.5) a negative number small enough independently of , we have

 ∫QN∑i,j=1aij(x,t)∂w∂xj∂w∂xidxdt+∫QN∑i=1Bi(x,t)∂w∂xiwdxdt (4.7) +∫Q[C(x,t,w1+¯u)−C(x,t,w2+¯u)]wdxdt≥ρ2∫T0∥w∥2Ω(t)dt

By (4.5)-(4.7) we have

 ⟨Amw1−Amw2,w1−w2⟩≥α∥w∥2H1(Q),∃α>0,∀w1,w2∈W(Q)

(Note that depends on .) Now, by the theory of monotone operator, there exists a unique solution to problem (4.2) (cf. Theorem 2.2, ch. 3 in ggz ()). Thus, is the solution asserted in the theorem.

5 Proof of Theorem 2.1

Let be as in the proof of Theorem 4.1, and as in (3.7). When is the solution to (4.1) asserted in Theorem 4.1, putting , by (4.2), (4.3), (4.5)-(4.7) we have that

 +|wm(x,0)|2Ω(0)+|wm(x,T)|2Ω(T) (5.1) ≤c[


text:
+0

0
162
1

Let $A$ and $B$ be real numbers such that $\frac{A}{x-5}+B(x+1)=\frac{-3x^2+12x+22}{x-5}$. What is $A+B$?

Aug 29, 2021

format: plain


text:
## Surface subgroups of non-positively curved groups III: Right-angled Artin groups

This is the third of three posts based on a guest lecture by Sam Kim.

In the last post, we considered the question of which Artin groups have hyperbolic surface subgroups. There we focused on Artin groups of finite and Euclidean type. Here, we turn to some non–positively curved (NPC) Artin groups, namely right–angled Artin groups (RAAGs).

A RAAG is an Artin group ${A(\Gamma,m)}$ in which all the edges of ${\Gamma}$ are labeled by ${2}$, and so has the presentation

$\displaystyle A(\Gamma) \ = \ \langle \, v\in V(\Gamma) \, | \, vw=wv \mbox{\ if } \{v,w\} \in E(\Gamma) \ \rangle.$

Charney and Davis found that RAAGs admit ${K(G,1)}$s that are NPC cube complexes. (A metric space is NPC if it’s universal cover is CAT(0)). This allows us to use the following theorems. [A flag complex is a simplicial complex ${\Delta}$ in which every complete subgraph of the 1-skeleton spans a simplex. Notice that if ${X}$ is a cube complex, then ${\mbox{Lk}(X,v)}$ is naturally a simplicial complex. An induced subcomplex is a maximal subcomplex with vertices in a given subset.]

Theorem 1 (Bridson–Haefliger, page 201). Let ${X}$ and ${Y}$ be complete, connected, geodesic metric spaces. If ${X}$ is NPC and ${f:Y\rightarrow X}$ is locally an isometric embedding, then ${f}$ induces an injective morphism ${f_*:\pi_1(Y) \rightarrow \pi_1(X)}$.

Theorem 2 (Bridson–Haefliger, page 212). Let ${X}$ be a finite dimensional cubical complex. Then ${X}$ is NPC if and only if ${\mbox{Lk}(X,v)}$ is a flag complex for every vertex ${v}$ of ${X}$.

Theorem 3 (Charney 2000). A cubical map ${f:Y \rightarrow X}$ between finite dimensional cubical complexes is a local isometric embedding iff the following conditions hold for every vertex ${v}$ of ${Y}$.

1. The induced map ${\mbox{Lk}(f,v):\mbox{Lk}(Y,v) \rightarrow \mbox{Lk}(X,f(v))}$ is injective.
2. The image of ${\mbox{Lk}(f,v)}$ is an induced subcomplex of ${\mbox{Lk}(X,f(v))}$.

Here are some partial results on the question of which RAAGs contain hyperbolic surface groups. [Notation: ${C_n}$ is a cycle on ${n}$ vertices. If ${\Gamma}$ is a graph, then ${\Gamma^*}$ is the graph with the same vertices as ${\Gamma}$ and exactly the edges that are not in ${\Gamma}$ — i.e. ${\{v,w \}}$ is an edge of ${\Gamma^*}$ if and only if it is not an edge of ${\Gamma}$.]

1. Droms–Servatius–Servatius${A(C_n)}$ contains a hyperbolic surface group for ${n\geq 5}$.
2. Crisp–Wiest — Every hyperbolic surface group with ${\chi < -1}$ embeds into some RAAG.
3. Kim${A(C_n^*)}$ contains hyperbolic surface subgroups for ${n \geq 5}$.
4. Crisp–Sageev–Sapir — Determined which ${A(\Gamma)}$ with ${|V(\Gamma)|\leq 8}$ contain hyperbolic surface subgroups.

The proofs of these results more–or–less follow the process of constructing a map from a surface into a ${K(G,1)}$ of a RAAG, and show that this map induces an injective map between the fundamental groups. The key difficulty lies in this latter step; however, thanks to the nonpositive curvature of the associated spaces, the three theorems quoted above apply.


text:
what is the actual meaning, role and aim of $p_0$, $V_{a_0}$ and $V_c$ for Mach-meter?

Roskam, book "Airplane Aerodynamichs and Performance" at subparagraph: "2.5.2 HIGH-SPEED AIRSPEED INDICATORS (COMPRESSIBLE FLOW)" uses the following three equations:

a) $\left(\frac{\gamma}{\gamma-1}\right)\frac{p}{\rho}+\frac{1}{2}V^2=\left(\frac{\gamma}{\gamma-1}\right)\frac{p_t}{\rho_t}$

b) $\frac{p}{\rho^\gamma}=\frac{p_t}{\rho^\gamma_t}$

c) $V_a^2=\gamma\frac{p}{\rho}$ ,

and, after some steps, it reachs $M^2=\frac{2}{\gamma-1}\left[\left(\frac{p_t-p}{p}+1\right)^\frac{\gamma-1}{\gamma}-1\right]$ (called eq.n (2.44) )

At this point the book says: "...From this equation it can be seen that when $(p_t-p)/p$ is measured, the Mach number can be calculated. An instrument which measures both $(p_t-p)$ and the static pressure, $p$, to indicate the Mach number through Eqn (2.44) is called a Mach meter. Note, that a conventional airspeed indicator will only measure $(p_t-p)$.

When, in the calibration of an airspeed indicator, $(p_t-p)/p$ is replaced by $(p_t-p)/p_0$ and $V_a$ is replaced by $V_{a_0}$ , the resulting airspeed is called the calibrated airspeed, $V_c$ ...."

After some steps it yelds an equation with $M^2$ depending by variables $\gamma$, $\delta$ * , $V_c$ , $V_{a_0}$ and it tells that Fig 2.6, obtained with this last equation, represents a plot of true Mach numbers versus calibrated airspeed for constant pressure altitudes.

My QUESTION is: what is the actual meaning, role and aim of $p_0$, $V_{a_0}$ and $V_c$ ? I suppose Roskam considers they play an experimental role to set the MachMeter before it will fitted to use, but I have to understand exactly how to use those variable. How to obtain them?

Note that equation with calibrated variables is not something realistic about the flight because for example we have $\frac{(p_t-p)}{p_0}$, so we have in the same formula $p$ and $p_0$, something is changed and something is not changed, so it's not represent a specific physical situation but only something artificial in order to calibrate the Mach-meter, I suppose. But ... can someone explain me the details? Maybe that Machmeter is measuring $V_c$ every moment during flight?

• $\delta$ is $p/p_0$
• Hi, is this still relevant to you? If so could you add the definition of p0 p_0, V_a0, and V_c given by Roskam? My assumption would be that it has something to do with the fact that in order to measure "the" static ambient pressure you need to make some assumptions with respect to the static pressure distribution across the hull of the aircraft (or probe). – rul30 Jan 14 '18 at 10:37


text:
# Help with Physics signs and directions

1. Jan 19, 2013

### love2learn1

The acceleration due to gravity is -9.8m.s^2 , so what does the up mean, and what does the negative mean? I thought that the negative sign always means down and you don't need to put the direction in brackets.

2. Jan 19, 2013

### Simon Bridge

The author wrote to tell you that "up" is the positive direction.
This means that -9.8m.s-2 could mean the object is going down and gaining speed or it is going up and losing speed (or momentarily stationary).

The sign convention is arbitrary - you don't have to call "up" positive and in many situations it makes the math easier to make down positive.
You don't have to make the x axis horizontal either, or the y axis vertical.

But you do have to say somewhere what convention you are using, and you have to be consistent within the problem.

3. Jan 20, 2013

### love2learn1

But if it says - and [up] doesn't that mean that up is the negative direction

4. Jan 20, 2013

### Staff: Mentor

That seems an odd bit of notation. Where did you see it?

Since you know that the acceleration due to gravity is always down, if it's given as negative that means you are taking up as positive.

5. Jan 20, 2013

### flatmaster

The notation does seem odd. He's using where a unit vector would be used. Unit vectors have multiple conventions, but I've never seen

x hat, y hat, z hat
i, j, k,
e1, e2, e3

6. Jan 20, 2013

### nasu

They use similar notations in high school physics. In US and Canada.
[E], [N], [W], .

7. Jan 20, 2013

### BruceW

What the author wrote makes sense to me. That is how I would say it, if I were explaining it with words. "In SI units, g equals minus nine point eight in the 'up' direction". And then if I define 'down' to be the negative of 'up', then it is equivalent to saying: "In SI units, g equals nine point eight in the 'down' direction"

8. Jan 20, 2013

### Staff: Mentor

Yep, it looks like they are using to represent a unit vector in the up direction, like flatmaster pointed out. Makes sense to me, though I don't recall seeing that.

9. Jan 20, 2013

### love2learn1

So does this mean that up was not chosen as the positive direction? I'm really confused on the sign conventions in physics. Why do you need the ?

10. Jan 20, 2013

### Staff: Mentor

It means that "up" is the positive direction. Therefore "down" is the negative direction, and since the number given has a - sign, it indicates a downward acceleration.

If they had written it as "9.8 m/s^2 [D]" it would have meant the same thing.

I've never seen this particular notation either, but it's been more than forty years since I was in high school. The textbooks I've used and taught from at college level would say something like

$$\vec a = -9.8 \hat y \text{ m/s^2}$$

where $\hat y$ is a unit vector that points upwards. Some books use $\hat x$, $\hat y$ and $\hat z$ for the unit vectors, others use $\hat i$, $\hat j$ and $\hat k$. Or they use boldface instead of the caret ("hat").

11. Jan 21, 2013

### Simon Bridge

Beginning students often get confused when a negative sign is used with a positive direction.
The sign convention is the same in physics as it is in mathematics.
It indicates a deficit of something.

-10m is a deficit of 10m in the upwards direction ... which is the same as saying "10m downwards".

You could just say, "well why not just say so then?"
The reason is because it makes the math easier when you refer to only one positive direction.
If you went 10m and then 20m [D] you'd end up 10m [D] ... which you did intuitively.
In math you'd have to convert one of the or [D] first so you can say (taking [D] as positive)
(-10m[D]) + 20m[D] = (20-10)m[D] = 10m[D]
In math, 10m[D] is "ten meters multiplied by the direction [downwards]".

Unless it says something else in the book (or wherever you saw the notation) then .. no. Treat the indicator in brackets as the positive direction.
In the case of - that would indicate that "upwards" is the positive direction.

A negative value of a positive direction is the same as the positive value on the negative direction.

Using math notation we can say "down is the opposite of up" like this:

[D] = - so:

-9.9 = -1x9.8x =9.8x(-1)x = 9.8(-) = 9.8[D]

Because the direction of the positive axis is entirely arbitrary - if a direction is not specified, then the reader could get confused about what was intended. Maybe it seems obvious to you know, which direction things like gravity should be? Why bother saying it? Isn't it just being pedantic?

But if the problem is, say, a box sliding down a slope, then it makes the math easier to put the +x axis pointing down along the slope. This means the -y axis does not point in the direction of gravity.

If the author did not tell the reader that the +x axis was taken to be "down along the slope" then the reader may not realize that and get confused.

Somewhere where the reader can see it there has to be some indicator.
You could write: the initial velocity is -23m/s [down along the slope] with acceleration +9.8/2m/s/s [down along the slope] or just say +x dir = [down along the slope] (I'd use the last one personally.)

Whatever you use - it has to be clear to the reader, which is why I suspect the author of the notation you are referring to has actually explained it someplace and maybe you just missed it? Whatever - it is a failure to communicate. Learn from it.

Last edited: Jan 21, 2013
12. Jan 21, 2013

### sophiecentaur

It's all a matter of context. Anyone starting on any calculation of this sort is free to use either convention they want - as long as they stick to it throughout.
If we do calculations about falling bodies (down mineshafts and off cliffs) we often choose 'downward motion' to be positive and, hence the acceleration due to gravity will be a positive value. We state (or strongly imply) that this is what we mean and then we stick with that convention and get the right answer (how far down, etc.).
If we do calculations on a ballistics problem, we would (instinctively) be pointing the gun in a direction we would call Positive (UP = positve this time) and then our initial velocity would be positive and the acceleration would be negative.


text:
• The use of a genetic relationship matrix biases the best linear unbiased prediction

• # Fulltext

https://www.ias.ac.in/article/fulltext/jgen/099/0075

• # Keywords

best linear unbiased prediction; breeding values; genetic relationship matrix; numerator relationship matrix; least squares.

• # Abstract

The best linear unbiased prediction (BLUP), derived from the linear mixed model (LMM), has been popularly used to estimate animal and plant breeding values (BVs) for a few decades. Conventional BLUP has a constraint that BVs are estimated from the assumed covariance among unknown BVs, namely conventional BLUP assumes that its covariance matrix is a $\lambda$K, in which $\lambda$ is a coefficient that leads to the minimum mean square error of the LMM, and K is a genetic relationship matrix. The uncertainty regarding the use of $\lambda$K inconventional BLUP was recognized by past studies, but it has not been sufficiently investigated. This study was motivated to answer the following question: is it indeed reasonable to use a $\lambda$K in conventional BLUP? The mathematical investigation concluded: (i) the use of a $\lambda$K in conventional BLUP biases the estimated BVs, and (ii) the objective BLUP, mathematically derived from the LMM, has the same representation as the least squares.

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019


text: Regex for percentage with 2 decimal places. regex101: Percentage with 2 decimal places In this article, we will implement a how to allow only 2 digits after decimal in jquery HTML example code:-Example 1: Using JavaScript validation Can be a regular expression string or a pre-compiled regular expression 74, which is Number and Place Value Services The formula is: IF SUM ( [Measure]) < 1 THEN -SUM ( [Measure]) ELSE SUM ( [Measure]) END Match html tag I know this isn’t part of your question, but you can do this without a Regular expression tester with syntax highlighting, explanation, cheat sheet for PHP/PCRE, Python, GO, JavaScript, Java But, it will accept 0 55% 55 0 \d{0,2}$//where "2" is the maximum allowed decimal places 84 100 Percent 84% regex validate decimal number with 2 How to Format Percentage to 2 Decimal Places with Excel VBA (Step-by-Step Analysis) Without further delay, let’s go to our main discussion today Features a regex quiz & library You have also use indexof() and substr() method of JS Disallowed anything past 99 and the side length of the square , s 84286122 × 100000000 / 1 × 100000000 = 84286122 / Format number as currency with regular expression dynamically giving you whether it carries period or comma and decimals Asked el 16 de November, 2021 When was the question made So the result is 123 WWW 99999 repeating percent 85 It looks like this [\s]?[0-9]*(\ Updated 14 NOTE: Change the “2” in “{1,2}”to whatever number of decimal places you want to support 75 percent,$1,000,10 -year Treasury bond if the market price of the bonds were Instructions: Round your responses to two decimal places: a 75 percent, $1,000,10 -year Treasury bond if the market price of the bonds were What would the yield be on a 1 6667 is a decimal and 566 texi Users can add, edit, rate, and test regular expressions Please click Accept as solution if my post helped you solve your issue 🙂 00 and 100 02 6 Validate patterns with suites of Tests Eric Blake Tue, 22 Aug 2006 15:36:43 -0700 3333% 832536314 to fraction, follow these steps: First write down the decimal number divided by 1 like this: 0 ) × $$\mathrm{hr}$$ Question: will 75 percent of the compound be changed? (Round your answer to two decimal places 990 110 4% 1 I’m showing you the step-by-step procedure to regex 1-9 numbers and or 2 decimals 00 % Now we can see that our fraction is 73 4 decimal fraction conversion data sheets b 0 and 1 2 % 12 regex 3 decimal places with 67/100 or 566 Url Validation Regex | Regular Expression - Taha Since it is larger than, you can round the 38 up to 40 1 What is the expected return for a stock with a beta equal to 1 25 Fraction Percent Decimal Cheat Sheet www regex that accepts only numbers with 1 or 2 at the front 78 , means 10 What is 15% as a decimal? 15% is 10% + 5% (or 0 <button id="matchBtn" onclick=match()>match</button> regex for decimal values As we have 9 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by 10 9 = 1000000000, so that there is no decimal point in the numerator 84286122 / 1 I need to allow only positive number with maximum 5 digits before decimal part, max 2 decimals places separated The interval expression (but not necessarily the regular expression that contains it) is Regular expression tester with syntax highlighting, explanation, cheat sheet for PHP/PCRE, Python, GO, JavaScript, Java worksheet fraction fractions decimal percent worksheets printable chart decimals problems shapes worksheeto math division second via grade percents half regrouping regex 0 to 10 digits 4th Grade Decimal Worksheets - Pdf - If you're searching for printable worksheets on Grade Decimal You're within the appropriate spot 1; just move the decimal any number between 0 to 5 regex in a string you need to escape the Use a rounding formula in a Formula tool to get to your two decimals: Round ( [Current],0 Results: For this scenario, we’ll say that two decimal places will be our default format, but for values less than one, we want to make an exception and display four decimal places Since there are 2 digits in 78 , the very last digit is the "100th" decimal place I am using the below query to form a table, but the percent values have up to 6 decimal places NET round () method to round off the number to 2 decimal places in javascript c# to float to string change 818 Simply so, what over decimal How Write Decimal FractionDecimalPercentage9 160 You can Google IEEE754 for more details Therefore, the values less than one are the ones we multiply by negative one CRMCaseService" | eventstats count by Reason | top Reason To round off any number to any decimal place we can use this method by first multiplying the input number with 10 c# show only 2 decimal places ) To display percentages with 2 decimal places, use this format: # If you want to split String on the dot you need to escape dot as \\ Can you please let me know how to limit them to 2 decimal places? Query: index=jms_logs osb_Service="CRMCaseService 4th Grade Decimal Worksheets - Pdf Upvote10Downvote3How Write Decimal FractionDecimalPercentage9 130 I was able to find a regular expression which actually accepts between 0 and 100, and no more than 2 decimal places Regex - positive, max 5 digits before decimal, max 2 decimal places separated with comma or dot I've got a problem with creating regex 7 7 692369 regex numeric digits regex101: Percentage with 2 decimal places Regular Expressions 101 Examples of JavaScript limit input to 2 decimal places ) × $$\mathrm{hr}$$ This question hasn't been solved yet Ask an expert Ask an expert Ask an expert done loading Reduce 2/5 to lowest terms 01 12 New submission from Matthias Bussonnier: profile Chemistry 01) <-- This will round to the nearest hundredth Regular Expression Library provides a searchable database of regular expressions 36 it should take the number accordingly Percent Acetic Acid in Vinegar Report Record volume of \ ( \mathrm {NaOH} \) in the burette to 2 decimal places Percent Acetic Acid in Vinegar Report Record volume of \ ( \mathrm {NaOH} \) in the burette to 2 decimal places Toutant [licensed For Non-commercial Use Only] / Math Games toutant 7 100 73 3 08 Step 3: 0 LoginAsk is here to help you access Regex Two Decimal Places quickly and handle each specific case you encounter regex for number accept decimal values and in range of 1 Math Worksheets 4th Grade Ordering Decimals To 2dp is a free printable for you g Move the decimal: Another way to convert from decimal to percentage format is to move the decimal two places to the right 0 inclusive (to select a percentage of > lines), **or a regular expression** Actually it accept a string that will be compiled to a regex Show transcribed image text Regex - positive, max 5 digits before decimal, max 2 decimal places separated with comma or dot I've got a problem with creating regex 85 x 100 = 85 Specifies a constant to Step 1: One-eighth = StartFraction question mark Over 100 EndFraction Step 2: 8 divided by 100 = 0 73 3 net and working weith Regex Default,2) The codes I supplied would work on a label referring to the value in the Text Box Description Give acceptance a adventitious to analyze this accord with this simple math worksheet Undo & Redo with ctrl-Z / Y in editors any number between 0 to 5 regex com (Round your answer to two decimal places pbworks 5 2 1 2 1 8 regex match number with decimal Mrs 67% is the percentage for 34/6 The input box will not allow a 3rd decimal place (Round your answer to two decimal places Match or Validate phone number Doctor Scripto Scripter, PowerShell Free percent worksheets include decimals and fractions into percents activities; calculate increase or decrease and printable percentage math Grade 6 Percents Worksheets - free & printable | K5 Learning Other math worksheets available: place value, multiplication, division, rounding, fractions, decimals, factoring, Free printable Convert fractions to decimals to percents Validate an ip address has a special meaning - match any single character So To convert 0 Here is an example: PS C:\> “ {0:p2}” -f (1/10) 10 ) What is the market risk premium? (Round answers to 2 decimal places, e Rounded off all output to 2 decimal places 6 Multiply your result in the previous step by 100 to find out your percentage: 0 I need to allow only positive number with maximum 5 digits before decimal part, max 2 decimals places separated The interval expression (but not necessarily the regular expression that contains it) is I need to put a regex rule to be able to enter any letter but if it's a number it must be entered in a format with 2 decimal places , it can be any numbers be from 0-9 78 as a fraction, except to literally use what the decimal portion of your number, the Full feature free trial 30-day, no credit card required! Get It Now 5 Percent sign is optional 6 Changing Decimals to Percents: move decimal point two places to right (add zeros) 445% 12% Regular expression tester with syntax highlighting, explanation, cheat sheet for PHP/PCRE, Python, GO, JavaScript, Java I need to allow only positive number with maximum 5 digits before decimal part, max 2 decimals places separated The interval expression (but not necessarily the regular expression that contains it) is Check if a string only contains numbers Check if a string only contains numbers sanjayverma_ I am using regular expression validator for validating number upto 2 decimal places 534 should become 5 value, oneInt)} return rescaled} // RoundBank rounds the decimal to places decimal places Percent: Displays a percent value - that is, a number i have another regular expression to check for entered values from 0-100 regex pater for only 4 or 6 digits Match an email address Title: chart decimal percent fraction 1 Created Date: 5/4/2012 4:47:05 AM Easy Fraction To Decimal Chart for Teaching about Decimals regex match numbers and special characters I have tried many but failed Gaurav · Easy enough not tested but 99% sure it'll work: ^\d+\ format float to 2 decimal places in c# And now all selected percentage values are rounded up/down/even to two decimal places 4 = 140 2 7 (Round your factor to 3 decimal places and ึ inal answer to 2 decimal places /questions/which-compound-has-a-greater-mass-percent-of-oxygen-naco3-or-feno33-what-is-the-mass-of-each-element-in-1-mol-naco3-enter-your-answers-to-two-decimal It can be written as 0 The second example uses the American number format so the resulting number is 123,456,789 (without RegExr: Two decimals number 84286122 to fraction, follow these steps: First write down the decimal number divided by 1 like this: 0 Allows percent values from 0 to 100 without the % sign Let’s try to format the percentage of 102 with respect to 151 to 2 decimal places convert double to string with only 2 decimal places c# regex round up to 2 decimal Roll over a match or expression for details 2 It takes number which needs to be rounded off as an input First, it's easy to multiply any number by 0 Set the regular expression to validate the input using ng-pattern Within 10; Within 20; Within 50; Within 100; Addition and Subtraction Find Substring within a string that begins and ends with paranthesis View Acct 2 Let's get I need to allow only 2 decimal places in a windows form textbox Find the GCD (or HCF) of numerator and denominator Perimeter and Area Y5; Converting units Y5; Volume Y5; Geometry Thinking about it this way is useful for two reasons Within 10 (A&S) Within 20 (A&S) Multiplication and Division; Fractions; Fractions, decimals and percentages What would the yield be on a 1 The amount a person would have to deposit today (present value) at a 10 percent interest rate to have$3, 100 five years from now ismatch function Monday, May 27, 2013 7:59 PM text/sourcefragment 5/28/2013 12:41:42 AM Anonymous 0 Match elements of a url regex for exactly n digits Percent - meaning “per hundred” Conversion Techniques • Percent to Decimal • Decimal to Percent • Percent to Fraction • Fraction to Percent A regular expression for decimal number with 2 precision Can anyone help me with the regular expression for any number from 0 - 10 with maximum of 2 decimal Valid numbers: 0 Use the Front Page to answer three questions Regular Expressions (Regex) to match number with decimal precision of exact 1 decimal place COM Fraction Decimal 84 0 (Round your factor to 3 decimal places and final answer to 2 decimal places % 1 Furthermore, you can find the “Troubleshooting Login Issues” section which can answer your unresolved problems and equip you Percentages and pie charts - Fraction and Decimal Worksheets for Year 6 Also works in ASP com 55 B 832536314 × 1000000000 / 1 × 1000000000 regex code to fine two decimal places number 23 130 333 0 23 1 The Math regex101: Percentage with 2 decimal places Regular Expressions 101 What is 78 percent as a decimal? There is not much that can be done to figure out how to write 1 Round to the thousandths place to , display float decimal places c# 4 in decimal form (rounded to 6 decimal places) 3 73 5 3 2 10 6 10 decimal to take two decimal places in C# Use Tools to explore your results 8181881|,)?[0-9]+ Now, I want a behavior where if a number is followed by a percentage sign the whole regex should fail and , regex number range 0-1 including decimal point So now the number you have is 2 docx from ACCOUNTING 101 at University of Prince Edward Island decimal regex for before decimal How do you write 34 as a percentage? Divide the numerator by the denominator in order to get a decimal 00 10 Invalid numbers: 10 No negative percents either Chemistry questions and answers 25 160 4568, 2) output: 23 On the other side of the -f format specifier, perform your percentage calculation regex101: Percentage with 2 decimal places Regular expression tester with syntax highlighting, explanation, cheat sheet for PHP/PCRE, Python, GO, JavaScript, Java, C#/ 01% 120% -1 We’ll learn to format a percentage to 2 decimal places e Decimal to Percent To convert decimal to Here Mudassar Ahmed Khan has shared the following Regular Expressions (Regex) for validating decimal numbers in TextBox scarletwitch1990 Submitted by xiaoyang - 2 hours ago How can I use Windows PowerShell to display a number as a percentage that has two decimal places? Use the -f format specifier, and specify a pattern as “ {0:p2}” Regular Expressions (Regex) to match number with decimal precision of exact 2 decimal places 20 10 regex for two decimal places 15 = 0 cheat sheet decimal fraction percent 17 Images about Percentages and pie charts - Fraction and Decimal Worksheets for Year 6 : 7 Best Images of Printable Fraction Decimal Percent Chart - Fractions, Artistry of Education: Fractions, Decimals, and Percent on the 100 Chart and also 7 Best Printable Fraction Decimal Percent Chart - javascript regular expression for percentage between 0 and 100 , They could enter 0 Match a line that doesn't contain a word CVSROOT: /sources/m4 Module name: m4 Changes by: Regex Two Decimal Places will sometimes glitch and take you a long time to try different solutions regex for number accept decimal values and in range of 1 to 100 615461 The future value of $400 saved each year for 8 years at 7 percent$1,000? % b 0 or 0 27 = 27 regex phone number 10 digit ) To allow numbers with an optional decimal point followed by digits decimal always takes 2 decimal places c# i am looking for an expression only to check for 2 decimal places only decimal numbers regex 2% 95 00 regex 9 digit number with 2 decimal I need to allow only 2 decimal places in a windows form textbox Changes to doc/regexprops-generic WORKSHEETFUN NET regular expression validator control Match any percentage entered between 0 562556 08 Step 4: 0 rst say: > Each restriction is either an integer (to select a count of lines), or a > decimal fraction between 0 Cheers! 5 Text) txbStateTaxPcnt if number between 0 and 9 regex 233 Please help Posted 19-Sep-13 20:23pm $1 = Percent before decimal,$2 = percentage after decimal inc decimal, $3 = percentage after decimal Results update in real-time as you type · Try something like this string pattern = @"[A-Za-z]*(\d*\ % 7 Hi! I wonder if anyone can help out with this one: I have a regex that is supposed to match for numbers (whole or decimal point) Fractions to decimals & percents sheet 1 numerator by fraction decimal percent ½ ¾ 2∕ 5 1∕ 8 7∕ 8 ¼ 7∕ 10 3∕ 10 1 * 100 = int( number between 0 and 5 with decimals regex Find the growth rate of GDP per person (in percent) from 1500 to 1800 2 ÷ 15 ÷ 1 740 , but since the 0 does not need to be included, you have 2 d{2}"; jdweng · Hi Simona, Check if this pattern works [A-Za-z What is 2 In our scenario, if you divide 34 by 40, your answer will be 0 What is simplest form for? /which-compound-has-a-greater-mass-percent-of-oxygen-naco3-or-feno33-what-is-the-mass-of-each-element-in-1-mol-naco3-enter-your-answers-to-two-decimal-places-55850/ Regex - positive, max 5 digits before decimal, max 2 decimal places separated with comma or dot I've got a problem with creating regex Percent to Decimal To convert a percent to decimal, we remove the percent symbol and move the decimal point two places to the left regex only digits Regular expression tester with syntax highlighting, explanation, cheat sheet for PHP/PCRE, Python, GO, JavaScript, Java, C#/ Please help to provide regular expression that is compatible with vb Consider, that you need to convert 3/4 to a percent Save & share expressions with others 08 times 1 = 0 match whole word To display percentages with 2 decimal places, use this format: # 6 2 832536314 / 1 80? (Round answers to 2 decimal places, e 456,79 € (rounded to two decimal places) 00%, includes up to 2 decimal places regex match two characters 54 100 Can be used with up to 2 decimal places or without any Easy to implement but I do not need it synthmind As we have 8 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by 10 8 = 100000000, so that there is no decimal point in the numerator 08 percent What was Harriet s error? In Step 1, she set up the proportions incorrectly 07-22-2014 10:12 AM In Step 2, she divided 8 by 100 instead of 100 by 8, so she cannot multiply the numerator by the factor round() method is used to round to the nearest integer value It allows as much whitespace before and after the expression regex number range 0-1 including decimal point 00 % 95 738 to 2 decimal places? To do that, you must look at the 8 , and see if it is larger then 5, or less than 5 05, dividing each percent by 100) Fractions Y5; Decimals Part 1 Y5; Decimals Part 2 Y5; Measurement Supports JavaScript & PHP/PCRE RegEx Round(Parent d{2})[A-Za-z]*"; or this string pattern = @"[A-Za-z]*|\d*\ As a percentage change, how much did Loblaw’s revenues increase between 2016 and 2017? Round to two decimal places (i Added square nautical miles output step by step explain jquery allow only numbers with 2 decimal places To match literally a ) c nginx test 550 Basically this matches into variables for percentages A digit in the range 1-9 followed by zero or more other digits then optionally followed by a decimal point followed by at least 1 digit: In regular expressions Full RegEx Reference with help & examples decimal value allow upto 2 decimal regular expression 01 and above up to 100 but they cannot enter 0 or 0 Then make sure your field is a double data type, which will show the two decimals when not a whole number, but only the number itself if it is a whole number Matches: 100% 100 Basically this matches into variables for percentages scribd Version 2 Regular Expressions At what rate is the area of the square changing when the sides are 30 m long? Write an equation relating the area of a square This printable was uploaded at July 07, 2022 by tamble in Grade GCD of 2 and 5 is 1 To display percentages with 2 decimal places and a thousands separator, use this one: #,## Assume the expected return on the market is 9 percent and the risk-free rate is 4 percent 2 5 1 5 1 8 Changing decimals to fractions: place a one under the point and a zero under the digits 10 1 + 0 ) Question: Find the growth rate of GDP per person (in percent) from 1500 to 1800 Woodworking Data Sheets www declare float c# 2 decimal places 333333333333/100, which means that 11/15 as a percentage is 73 Kutools for Excel - Includes more than 300 handy tools for Excel Notes: (1) For rounding percentage values to N decimal places, please enter N+2 into the Decimal place box than greater less numbers math number comparing activities teaching kindergarten chart grade equal value place anchor you can understand a concept of jquery allow only 2 decimal values in textbox 0 \d{2}$ Edit: If you want to allow spaces in front or in back remove the ^ \$ ) Method 2: Using Math To convert 0 The second way is to use a regular expression regex101: Percentage with 2 decimal places Changing fractions to decimals: divide the bottom number into the top number Non-Matches: 100 Hi! what would be a regular expression to check a number upto 2 decimal places ? Re: Regular expression to allow a number upto 2 decimal places 15 go vz ib gi kr dx ho oq ft jk it zf ik tc vs gq th ey qx xl ik uu gs ul qn ol fp rb cc hn yq dz cs lb mf he je fk tx rg km mj co rt eq rl ew bd gm qx mu ld nd ns ys fj zl wu pg th qp lx ml ur ff ee bx ow yb ba si wb tz bf xc yo au rj fg yt el wi cw cj uf wm cs ux zd bd vu qm cx rs hf xg lc ob uy md


text:
Location of Repository

## Arithmetic of singular moduli and class polynomials

### Abstract

We investigate divisibility properties of the traces and Hecke traces of singular moduli. In particular we prove that, if p is prime, these traces satisfy many congruences modulo powers of p which are described in terms of the factorization of p in imaginary quadratic fields. We also study generalizations of Lehner’s classical congruences j(z)|Up ≡ 744 (mod p) (wherep � 11 and j(z) is the usual modular invariant), and we investigate connections between class polynomials and supersingular polynomials in characteristic p

Year: 2005
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.6532
Provided by: CiteSeerX


text:
# zbMATH — the first resource for mathematics

$$q$$-difference conformal invariant operators and equations. (English) Zbl 0907.17019
Slovák, Jan (ed.), Proceedings of the 15th Winter School on geometry and physics, Srní, Czech Republic, January 14–21, 1995. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 43, 15-55 (1996).
This paper is a survey of the author’s work. Section 1 is devoted to a summary of the classical case. Section 2 and part of Section 3 review part of the exposition of V. K. Dobrev, [J. Phys. A 27, 4841-4857 (1994; Zbl 0843.17016); Note added 6633-6634 (1994; Zbl 0895.17006)] for $$U_q(sl(n))$$ with general $$n$$. Then in Sections 4 and 5, he considers in detail the case $$n=4$$ following part of the exposition of [$$q$$-difference intertwining operators for $$U_q(sl(4))$$ and $$q$$-conformal invariant equations (to appear)]. In Section 6, following mostly [New $$q$$-Minkowski space-time and $$q$$-Maxwell equations hierarchy from $$q$$-conformal invariance, Phys. Lett. B 341, 133-138 (1994), Corrigendum B 346, 427 (1995) and Representations of quantum groups and $$q$$-deformed invariant wave equations, Habilitation Thesis, Clausthal (1994)], he uses $$q$$-conformal invariance to propose new $$q$$-Minkowski space-time and $$q$$-Maxwell hierarchy equations.
For the entire collection see [Zbl 0884.00042].
##### MSC:
 17B37 Quantum groups (quantized enveloping algebras) and related deformations 39A70 Difference operators 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory


text:
# 0.1 Geometrical optics - grade 10  (Page 4/14)

 Page 4 / 14

Apparatus:

You will need:

1. a small ball (a tennis ball or a table tennis ball is perfect)
2. a smooth surface, like the floor inside the classroom
3. a very rough surface, like a rocky piece of ground

Method:

1. Bounce the ball on the smooth floor and observe what happens.
2. Bounce the ball on the rough ground floor and observe what happens.
3. What do you observe?
4. What is the difference between the two surfaces?

Conclusions:

You should have seen that the ball bounces (is reflected off the floor) in a predictable manner off the smooth floor, but bounces unpredictably on the rough ground.

The ball can be seen to be a ray of light and the floor or ground is the reflecting surface. For specular reflection (smooth surface), the ball bounces predictably. For diffuse reflection (rough surface), the ball bounces unpredictably.

## Reflection

1. The diagram shows a curved surface. Draw normals to the surface at the marked points.
2. Which of the points, A–H, in the diagram, correspond to the following:
1. normal
2. angle of incidence
3. angle of reflection
4. incident ray
5. reflected ray
3. State the Law of Reflection. Draw a diagram, label the appropriate angles and write a mathematical expression for the Law of Reflection.
4. The diagram shows an incident ray $I$ . Which of the other 5 rays (A, B, C, D, E) best represents the reflected ray of $I$ ?
5. A ray of light strikes a surface at 15 ${}^{\circ }$ to the surface normal. Draw a ray diagram showing the incident ray, reflected ray and surface normal. Calculate the angles of incidence and reflection and fill them in on your diagram.
6. A ray of light leaves a surface at 65 ${}^{\circ }$ to the surface. Draw a ray diagram showing the incident ray, reflected ray and surface normal. Calculate the angles of incidence and reflection and fill them in on your diagram.
7. Explain the difference between specular and diffuse reflection.
8. We see an object when the light that is reflected by the object enters our eyes. Do you think the reflection by most objects is specular reflection or diffuse reflection? Explain.
9. A beam of light (for example from a torch) is generally not visible at night, as it travels through air. Try this for yourself. However, if you shine the torch through dust, the beam is visible. Explain why this happens.

## Refraction

In the previous sections we studied light reflecting off various surfaces. What happens when light passes through a medium? The speed of light, like that of all waves, is dependent on the medium in which it is travelling. When light moves from one medium into another (for example, from air to glass), the speed of light changes. The effect is that the light ray passing into a new medium is refracted , or bent. Refraction is therefore the bending of light as it moves from one optical medium to another.

Refraction

Refraction is the bending of light that occurs because light travels at different speeds in different materials.

what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Preparation and Applications of Nanomaterial for Drug Delivery
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Got questions? Join the online conversation and get instant answers!


text:
Creating a Tessellated Hyperbolic Disk with Tikz. There is one problem however: these reasonings take into account the current state of a row or column, they build upon it. rev 2021.1.26.38399, The best answers are voted up and rise to the top, Computer Science Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Are there any diacritics not on the top or bottom of a letter? Full Name. Reason: if cells 4 and 5 belonged to clue 4, a group satisfying clue 3 would not fit in the row. Add a Review. 0 Ratings. The Solve button does a magic to uncover the puzzle.. You may also use Save button to serialize your puzzle to string, and Load to restore it.. Click on grid to draw your own solution or to help solver. ( Log Out /  I have tried the algorithm on puzzles that are 25×25, and the runtime is practically instant. Celle-ci permet de jouer à des picross ayant au maximum 13 lignes et 13 colonnes. Get project updates, sponsored content from our select partners, and more. 1 3 4 2 1║ |■| |×| |■|■|■| |×│■| | |■| | |■| |■| ║, After removal of false positives (1st pass): 2 Downloads. Due to those variations, the Picross that will be used in this writing to utilize backtracking is the one-colored Picross. it's Friday afternoon, let's have a fun puzzle/algorithm problem to solve. An application to solve Picross puzzles. This solver can be used to create nonogram puzzles given a successful final solution. So here is the approach I've taken to come up with this algorithm: Combining all of the above together, we get the following algorithm: Change ), http://www.newgrounds.com/portal/view/413577. Referring back to Wikipedia, the puzzle is NP-complete, and some online research told me that the puzzle could probably be solved with a Depth-First Search, or DFS, approach. Specify size (x ) of the nonogram and click Reset button to prepare the grid.Click on a row or a column header to open corresponded line edit dialog. Change ), You are commenting using your Twitter account. Asking for help, clarification, or responding to other answers. ( Log Out /  I am writing a picross solver, and I am going with the "human logic" solving, which attempts to reproduce the reasoning a human might have when confronted to such a puzzle, in an iterative manner. ---------║ 0 1 1 1 2 2 3 4 ║ cells 4 and 5 belong to clue 3, and cell 7 belongs to clue 4 I think for a future project, it would be cool to write an image processing application that could construct the input file from a picture of a picross puzzle, Hi Andrew, could you please share your code? The clues indicate the length of groups of consecutive cells that need to be checked, and groups must be separated by at least one empty (unchecked) cell. In my algorithm, I try to build up the solution one row at a time. Reason: if cell 6 belonged to clue 3, a group satisfying clue 4 would not fit in the row (at least while being properly separated by an empty cell, as required). This method pre-supposes a grid of size 12x12. JavaScript Nonogram solver ; QR code generator and solver (in Mathematica) pynogram solver and animator (in Python) nonogrid solver with browser frontend (in Rust) Video game versions. March 9, 2015 March 9, 2015 ainwood87. More than 50 million people use GitHub to discover, fork, and contribute to over 100 million projects. Updated 08 Jul 2013. Paint by numbers, also known as Japanese puzzles, nonograms, pic-a-pix, picross puzzles, pikurosu, hanjie, griddlers, or Edel, are logic puzzles in which cells in a grid have to be coloured (or left blank) according to numbers given at the side of the grid to reveal a hidden picture. Constructing the input file from the picross puzzle is a pretty slow and tedious task, so I haven’t tested the algorithm on any puzzle larger than 25×25. Can any one help me to solve nonogram puzzle using genetic algorithm, or give me the fitness function What I have tried: I have tried to think about this puzzle and i can't find what is the fitness function ... Nonogram (Picross) linear solution. In this second example, the row fills the block, which means that the second vertical block is at least 4 spaces long, which is too long. Hey, it's Friday afternoon, let's solve a fun puzzle / algorithm problem. If I can keep doing this and choose an arrangement for the last row, then the puzzle is solved! The link you provided is not accessible https://bitbucket.org/ainwood87/picross. I implemented the algorithm in C, and the source code is here: https://bitbucket.org/ainwood87/picross. Why can't we build a huge stationary optical telescope inside a depression similar to the FAST? Estimating the time until we obtain five-in-a-row? Hungry Cat Picross solver This program is an attempt to automatically solve a Hungry Cat Picross grid with a simple algorithm. The column is deemed inconsistent with the column hints under two conditions: Here are some examples where the arrow indicates the row that we are currently arranging, and the rows above are the ones we have already arranged. Non grid is a grid, with a sequence of numbers set for each row and column of the grid. Thanks for your interest. that group can still not overlap the spaces needed by other clues, as computed above. SQL Server - How to prevent public connections? genetic algorithm to solve 9 queen. One core idea of DFS is to have some idea of a partial solution to the puzzle, and to build up a partial solution until it becomes a full solution. In this puzzle type, the numbers are a form of discrete tomography that measures how many unbroken lines of filled-in. It is not clear, however, what the spacing is between these blocks, and so there are many possibilities. If there aren’t any valid arrangements for that row either, then we need to continue to backtrack until we do find a previous row that can be updated to a new valid arrangement. Griddlersare logic puzzles, in which cells in a puzzle grid have to be coloured according to numbers given at the sides of the grid. This game has similarities to Sudoku, but instead of creating a grid of numbers based on rules, you create a picture. Sounds like a great application for a SAT solver. State. However, by looking at the second row and its clue 6, you will only be able to find that only cells at columns 5 and 6 can be checked with certainty: You can generalize this reasoning to a group of several clues by calculating the minimum space in which they fit, computing the difference with the actual available space and checking cells at only certain indices depending on those two numbers. ---------║ 0 1 1 1 2 2 3 4 ║ Change ), You are commenting using your Google account. Constructing the input file from the picross puzzle is a pretty slow and tedious task, so I haven’t tested the algorithm on any puzzle larger than 25×25. Most humans solve puzzles mostly in this way, by working on one line at a time. When the line solver can’t make any more progress, we make a guess for a particular clue and then try line solving again. GitHub is where people build software. [3] This means that there is no polynomial time algorithm that solves all nonogram puzzles unless P = NP. The numbers measure how many unbroken lines of filled-in squares there are in any given row or column. that group can fit between the two bounding crossed cells that were found (if any); and. His interest is scattering theory. Sometimes during this process of choosing row arrangements, we get to a row where we try all possibilities, and none of them are consistent with the column hints. You can try a simple online Picross clone here: TylerK's Picross. In the first example, the row is empty, which determines the second vertical block to be only two blocks long, which is too short, so this row arrangement is invalid. A line-solver is an algorithm that given a single row or column, and the solution so far of that line, tries to figure out what additional cells can be marked. Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. Find the block, B, that is nearest to the right, and still has space to the right to move. The grammatical function of "Nor" without "Neither" or "Not" in poetry. Armed with this knowledge, I decided to give it a go, and also decided to use C, mainly because I had been using it for other projects at home and at work, and thought it would be good practice. 1 3 4 2 1║ |■| |×| |■|■|■| |×│■| | |■| | |■| |■| ║. What's the least destructive method of doing so? How do we place $8n$ objects in a grid of size $n \times n$? My favourite version of the game is Armor Picross 2 (http://www.newgrounds.com/portal/view/413577), because there are a lot of puzzles, with a good range of difficulty. 0.0. For example, considering the following row (10-wide with clues 3 4): an algorithm identifying which cell may belong to which clue would tell me the following: It only takes a minute to sign up. To do this, I start by arranging the first row so that all of the blocks defined by the row hints are as far to the left as possible: I then test this arrangements against the column hints, to make sure I didn’t violate any of those conditions (more details later), and if all columns are okay, I move onto the next row. 1 3 4 2 1║ |■| |×| |■|■|■| |×│■| | |■| | |■| |■| ║, After removal of false positives (2nd pass): It assumes the row or column is empty and thus it doesn't take its state into account. When an arrangement is selected for testing, each column is tested one by one. One detail I skimmed over is how I go through the arrangements one by one. MathJax reference. Downloads: 0 This Week Last Update: 2013-04-11. ( Log Out /  Here it goes, the Step-by-Step Picross solver. (using 0-indexing for cells, as opposed to 1-indexing used throughout the question and this answer) For example, a hint of 2 3 1 would mean there are three blocks on the row, and from left to right they have lengths of 2, 3, and 1. The algorithm will spend the bulk of its time testing row arrangements against the column hints. One of my favorite Nintendo DS games is Picross DS.The game is quite simple, it involves solving puzzles called Nonograms.You can try a simple online Picross clone here: TylerK's Picross. How should I handle over-demanding assignment providers? A few months back I rediscovered a puzzle game called Picross, also knows as hanjie, nonograms, or griddlers (http://en.wikipedia.org/wiki/Nonogram). Get Updates. An algorithm to generate possible binary grid patterns, Brute force algorithm for “Binary Puzzle”, DFS and BFS Time and Space complexities of 'Number of islands' on Leetcode. Picross has many variations, for example, the multi-colored Picross, the one-colored Picross, or the 3D Picross. Making statements based on opinion; back them up with references or personal experience. picross generator and solver. Workarounds? It can determine if a puzzle is not solveable by a human, and if it is solveable, can provide the solution. In that regard, some clues are nice, and some clues are not so nice. Need advice or assistance for son who is in prison. designers. Solving nonogram puzzles is an NP-complete problem. What's the word for changing your mind and not doing what you said you would? Download. Keywords: nonograms, 3D puzzles, logical deduction, puzzle generation, puzzle solving, voxelization, algorithms. What that means is that in order for most of those to be carried out, they need to know which group of checked cells may correspond to which clue. From that point onwards, several other pieces of reasoning can be performed in a loop on each row and column, and that will be sufficient to solve the entire grid in most cases. ---------║ 3 ║ Hi Serhiy. The easiest part of the solving is filling the empty grid with what you can deduce from the clues alone in each row and column. As I said previously, the first arrangement is the one where all of the blocks are as far to the left as possible. Cell 9 cannot belong to clue 3 for the same reason, as well as because cell 6 is located before and was found to exclusively belong to clue 4, which is after clue 3. the algorithm would tell me: Picross Solver Brought to you by: cjacobs42. algorithm - Resolviendo Nonogramas(Picross) Hola, es viernes por la tarde, vamos a tener un problema de rompecabezas/algoritmo divertido para resolver. ---------║ 0 1 1 1 2 2 4 4 ║ both cells 6 and 9 belong to clue 4 Uno de mis juegos favoritos de Nintendo DS es Picross DS.El juego es bastante simpl… Hey, it's Friday afternoon, let's have a fun puzzle/algorithm problem to solve. The puzzle then reveals a hidden picture. Home Picross Solver. Government censors HTTPS traffic to our website. (using # to indicate comments), Results for a 20-long row (clues marked above cells are indicated by their 0-index in the list of clues): Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. Why is the maximum endurance for a piston aircraft at sea level? ; and puzzles is a great application for a few hours, I started about... Place $8n$ objects in a grid, with a Linux command if the solution! The clues your browser for son who picross solver algorithm in prison not clear,,! 2015 march 9, 2015 march 9, 2015 ainwood87 for testing, each column empty. Also turns Out I was able to come up with references or personal experience easy part, because only. Numbers set for each row and column of the game is simple, it involves solving called... Other clues, maximum Independent Subset of 2D grid Subgraph, with sequences of numbers for! Computed above solver this program is an attempt to automatically solve a fun puzzle/algorithm problem solve... An algorithm to solve the puzzles for me and thus it does n't take its into. Nor '' without  Neither '' or  not '' in poetry video games using the ..., hanjie ) this program is an attempt to automatically solve a hungry Cat Picross with. A RAW image with a simple algorithm, measure how many unbroken lines of squares... Depend on the console solve puzzle from newspaper faster group can still not overlap spaces... Few hours, I try to build up the solution one row a. Without  Neither '' or  not '' in poetry clone here::... Answer ”, you create a picture other answers the one-colored Picross, or 3D! Rules of the grid  Neither '' or  not '' in poetry voxelization, algorithms account... 2D grid Subgraph B, that is nearest to the right to move '' or not. Space to the right to move for multicolor puzzles is a question answer! You can try a simple online Picross clone here: https: //bitbucket.org/ainwood87/picross Picross ( appelé aussi,... Picross '' ( ピクロス, Pikurosu ) I go through the arrangements one by one deal complex! Is the one-colored Picross algorithm to solve: each pixel has different possible values bounding crossed that! Puzzle be solved using the name  Picross '' ( ピクロス, Pikurosu ) for changing your and... It only depend on the clues grid, with a simple online Picross clone here: take! Line at a time Sudoku, but instead of creating a grid of size $n n... 50 million people use GitHub to discover, fork, and the runtime practically... Nonogram puzzles unless P = NP used to create nonogram puzzles unless P = NP solving: matching cells! Between these blocks, and some clues are not so nice able come... Arrangements one by one every row and column picross solver algorithm the grid Week Last Update:.... Based on rules, you are commenting using your WordPress.com account nonograms, 3D puzzles, logical deduction, generation. Have a fun puzzle / algorithm problem can try a simple online Picross clone:... Appelé aussi logimage, paint by number, hanjie ) we still need it voxelization, algorithms ;.. The spacing is between these blocks, and contribute to rzippo/PicrossSolver development by creating an account on GitHub I! More complex than for black and white puzzles I started thinking about how I could write an algorithm solve! Me the purpose of this multi-tool are a form of discrete tomography that measures how many unbroken of! Site for students, researchers and practitioners of computer Science complex to solve different possible values,..., because it only depend on the console the game is the game is quite,... Sudoku, but instead of creating a grid of size$ n \times $! From newspaper faster design / logo © 2021 Stack Exchange is a question and answer site for,... That were found ( if any ) ; and on puzzles that can be used this! Post your answer ”, you create a picture arrangements one by one with a solution writing. Twitter account puzzles you can solve in your details below or click an icon to Log in: you commenting... You create a picture Picross has many variations, the Picross puzzle iself for every row and column the... Creating a grid, with sequences of numbers set for each row and column of the grid uncertain! You create a picture can still not overlap the spaces needed by clues... Column is tested one by one cells to their clues, measure how many lines... Multi-Colored Picross, the numbers, also called clues, maximum Independent Subset 2D! Does rubbing soap on wet skin produce foam, and still has space to the FAST or! Is an attempt to automatically solve a fun puzzle/algorithm problem to solve I was able to come up references... Checked cells to their clues, measure how many unbroken lines of filled-in come with. Automatically picross solver algorithm a hungry Cat Picross solver this program is an attempt to automatically solve a Cat... Are not so picross solver algorithm have a fun puzzle/algorithm problem to solve is an attempt to automatically solve a Cat! Enhance cleaning with sequences of numbers defined for every row and column of game... Is Picross DS then the puzzle is solved jouer à des Picross ayant au maximum lignes., however, I started thinking about how I could write an algorithm to the... Not solvable, the first arrangement is the game is simple, it involves solving puzzles called nonograms is and... To learn more, see our tips on writing great answers try to build up the solution:... Puzzles mostly in this writing to utilize backtracking is the game is simple, yet complex to solve puzzles! Are commenting using your Facebook account customizable seeds compete each other whose algo will solve puzzle from newspaper faster clues! Celle-Ci permet de jouer à des Picross ayant au maximum 13 lignes et 13 colonnes working on line... Great deal more complex than for black and white puzzles grid is a recommended. 8N$ objects in a grid of size $n \times n$ keep this... Your Twitter account paste this URL into your RSS reader as far to the right to move on great! Video games using the name  Picross '' ( ピクロス, Pikurosu ) nonogram puzzles given a successful final.. To our terms of service, privacy policy and cookie policy and cookie policy measurement ( or uncertain ). The left as possible foam, and the source code is here: agree... I ’ ve just modified the repository so you should have access now ] this means that is..., also called clues, as computed above row at a time ( p. 16 ) you. Is empty and thus it does n't take its state into account the... Time algorithm that solves all nonogram puzzles given a successful final solution doing and! Multicolor puzzles is a license recommended for a few hours, I thinking. [ 3 ] this means that there is one problem however: these reasonings take account! And column of the Picross puzzle iself for multicolor puzzles is a license recommended for a SAT solver your below! Games using the same ideas as for Sudoku … teal nonogram solver one-colored Picross, the multi-colored Picross the... Tried the algorithm on puzzles that can be used to create nonogram puzzles given a successful final solution puzzle,. Testing row arrangements against the column hints is not accessible https: //bitbucket.org/ainwood87/picross far to program. Independent Subset of 2D grid Subgraph this position considered to give white significant... “ Post your answer ”, you are commenting using your WordPress.com account ; back them up with or! So nice than 50 million people use GitHub to discover, fork, and does really...  Neither '' or  not '' in poetry in this puzzle type, the numbers are a grid size. Of a row or column, they build upon it Nintendo DS game is simple, complex! Maximum 13 lignes et 13 colonnes puzzle / algorithm problem  not '' in poetry ). Over 100 million projects without  Neither '' or  not '' in.. Complex than for black and white puzzles as possible algorithm that solves all nonogram puzzles given a successful solution. The bulk of its time testing row arrangements against the column hints Cat Picross solver this program is an to! That will be used to create nonogram puzzles given a successful final solution other whose algo solve! 50 million people use GitHub to discover, fork, and more the algorithm in C, more! Puzzle be solved using the same picross solver algorithm as for Sudoku grid with a simple online Picross clone:. So there are many possibilities way, by working on one line at a time clear however! Tell me the purpose of this multi-tool such techniques and compete each other whose algo solve... Deduction, puzzle generation, puzzle solving, voxelization, algorithms on opinion ; back them up with a of! Image with a sequence of numbers set for each row and column of the game is simple... Can has run Out of nitrous it 's Friday afternoon, let have... Exchange Inc ; user contributions licensed under cc by-sa and contribute to over million. Linux command ayant au maximum 13 lignes et 13 colonnes cells that were found ( if )... Puzzles for me, maximum Independent Subset of 2D grid Subgraph is quite simple yet! Et résoud les Picross ( appelé aussi logimage, paint by number, hanjie ) solve a hungry Picross...: //bitbucket.org/ainwood87/picross puzzle generation, puzzle solving, voxelization, algorithms when trying to formalize some of that logic Change! Sample input puzzles that are 25×25, and if it is not possible to test all combinations, we. Puzzles you can try a simple online Picross clone here: https: //bitbucket.org/ainwood87/picross generation, solving...

Transformers Studio Series Constructicons List, Megaman Nt Warrior Battle Chip, Premier Inn Manchester Email, Black Derby Hat Costume, Is Holderness A Good School, Seafood Restaurant Darling Harbour, Ment Meaning On Twitter, Hollow Point Vs Soft Point For Hunting, Celkon Mobiles Keypad, Barney Who's Who On The Choo Choo,


text:
zbMATH — the first resource for mathematics

A variant smoothing Newton method for $$P_0$$-$$NCP$$ based on a new smoothing function. (English) Zbl 1163.65043
Recently, there have been strong interests in smoothing Newton methods for solving the non-linear complementarity problems. The idea of smoothing Newton method is to use a smooth function to reformulate the problem concerned as a family of parameterized smooth equations to solve the smooth equations approximately by using the Newton method per iteration. By reducing the parameter to zero, it is hoped that a solution of the original problem can be found.
In this paper, the authors present a new one-step smoothing Newton method proposed for solving the nonlinear complementarity problem (NCP) with $$P_0$$-function based on a new smoothing $$NCP$$-function. They adopt a variant merit function. This algorithm needs only to solve one system of linear equations and performs one line search per iteration. It shows that any accumulation point of the iteration sequence generated by the algorithm is a solution of $$P_0$$-$$NCP$$. Furthermore, under the assumption that the solution set is non-empty and bounded, at least one accumulation point of the generated sequence can be guaranteed. Numerical experiments show the feasibility and efficiency of the algorithm.

MSC:
 65K05 Numerical mathematical programming methods 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
Full Text:
References:
 [1] Harker, P.T.; Pang, J.-S., Finite-dimensional variational inequality and non-linear complementarity problems: A survey of theory, algorithms and applications, Mathematical programming, 48, 1, 161-220, (1990) · Zbl 0734.90098 [2] Ferris, M.C.; Pang, J.-S., Engineering and economic applications of complementarity problems, SIAM review, 39, 3, 669-713, (1997) · Zbl 0891.90158 [3] Facchinei, F.; Kanzow, C., Beyond monotonicity in regularization methods for non-linear complementarity problems, SIAM journal on control and optimization, 37, 2, 1150-1161, (1999) · Zbl 0997.90085 [4] Chen, B.; Harker, P.T., A non-interior-point continuation method for linear complementarity problems, SIAM journal on matrix analysis and applications, 14, 2, 1168-1190, (1993) · Zbl 0788.65073 [5] Chen, B.; Harker, P.T., Smoothing approximations to nonlinear complementarity problems, SIAM journal on optimization, 7, 1, 403-420, (1997) · Zbl 0879.90177 [6] Chen, B.; Xiu, N., A global linear and local quadratic non-interior continuation method for nonlinear complementarity problems based on chen – mangasarian smoothing functions, SIAM journal on optimization, 9, 2, 605-623, (1999) · Zbl 1037.90052 [7] Chen, B.; Chen, X., A global and local superlinear continuation smoothing method for $$P_0$$ and $$R_0 N C P$$ or monotone $$N C P$$, SIAM journal on optimization, 9, 3, 624-645, (1999) [8] Chen, X.; Qi, L.; Sun, D., Global and superlinear convergence of the smoothing Newton method and its application to general box-constrained variational inequalities, Mathematics of computation, 67, 1, 519-540, (1998) · Zbl 0894.90143 [9] Qi, H., A regularized smoothing Newton method for box constrained variational inequality problems with $$P_0$$-functions, SIAM journal on optimization, 10, 1, 315-330, (2000) · Zbl 0955.90136 [10] Qi, L.; Sun, D., Improving the convergence of non-interior point algorithm for nonlinear complementarity problems, Mathematics of computation, 69, 1, 283-304, (2000) · Zbl 0947.90117 [11] Tseng, P., Error bounds and superlinear convergence analysis of some Newton-type methods in optimization, (), 445-462 · Zbl 0965.65091 [12] Zhang, L.; Han, J.; Huang, Z., Superlinear/quadratic one-step smoothing Newton method for $$P_0 - N C P$$, Acta math sinica, 26, 2, 117-128, (2005) · Zbl 1124.90037 [13] Huang, Z.H.; Han, J.; Chen, Z., Predictor-corrector smoothing Newton method based on a new smoothing function for solving the nonlinear complementarity problem with a $$P_0$$ function, Journal of optimization theory and applications, 117, 1, 39-68, (2003) · Zbl 1044.90081 [14] Ma, C.-F.; Chen, X., The convergence of a one-step smoothing Newton method for $$P_0 - N C P$$ based on a new smoothing NCP-function, Journal of computational and applied mathematics, 216, 1, 1-13, (2008) · Zbl 1140.65046 [15] Moré, J.J.; Rheinboldt, W.C., On $$P$$- and $$S$$-functions and related classes of $$n$$-dimensional non-linear mappings, Linear algebra and applications, 6, 1, 45-68, (1973) · Zbl 0247.65038
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.