The Harvard-Rand researchers believe the crisis may be partly fueled by inappropriate prescription practices for conditions that do not warrant treatment with opioids.
Researchers analyzed data for more than 800 million opioid prescriptions over a 10-year period.
But now, research shows that in almost a third of cases there's no medical reason documented for opioids prescribed in an outpatient setting. The drug, albeit legal, poses serious risks for abuse, dependence, and overdose.
Once a patient is addicted, it becomes hard to stop.
The CDC estimated back in August a record number of people died from drug overdoses in 2017.
According to the National Institute of Drug Abuse, more than 115 people die each day in the USA after overdosing on opioids. Since 1999, over 630,000 have died from an overdose.
The study was published September 10 in Annals of Internal Medicine. The NAMCS, a cross-section survey of patients' visit to physicians, report details from the meeting including prescribed medication.
In total, opioids were given in nearly 809 million outpatient visits. The other five percent treated cancer-related pain.
Of the prescriptions and not utilizing a narrative of disaster, the most abnormal conditions had been excessive blood stress, excessive cholesterol and opioid dependancy (2.2 %). The remaining 28.5 percent had no pain diagnosis at all. She's an instructor in medicine at Harvard and an associate physician at Brigham and Women's Hospital in Boston. That finding, the researchers say, highlights the need for periodic reassessment of the medical need to refill an opioid prescription.The researchers say their results underscore the need for stricter requirements on documenting the need for opioids-;an approach many insurance providers already use to determine approval of new, costly drugs.
Of the prescriptions for non-cancer pain, the most common conditions included back pain, diabetes and arthritis. Those who experienced no pain but were given prescription opioids reported hypertension, hyperlipidemia, opioid dependence, and other follow-up examination. There was not enough information to make that judgment, Sherry said.In many cases, physicians prescribed opioids without a clear understanding of how addictive those medications were. It is also possible that the prescription was "not clinically appropriate".
However, she clarified that the study does not mean that all transactions not backed with records were because of "nefarious goal on the part of the doctor".
Previous year the U.S. Department of Health and Human Services declared a public health emergency after discovering that 2.1 million people had an opioid disorder in 2016.


As he embarks on his 11th season as head coach and 29th year with the Florida Atlantic University baseball program, John McCormack has inked a five-year contract extension.
"Coach McCormack has done an incredible job of making FAU not only one of the top programs in C-USA but also nationally, and we are thrilled our program will be under his leadership for many years to come," said FAU Vice President and Director of Athletics Brian White."
In 10 years at the helm of the FAU program, McCormack has amassed 360 wins and a .618 winning percentage, leading the Owls to five NCAA regional appearances. His squads have won three conference regular season titles and one postseason league championship. Under McCormack's tutelage, FAU has had seven players earn All-America status, 14 All-Region selections and 35 All-Conference honorees. A total of 30 Owls have gone on to be Major League baseball draft picks since McCormack took over as head coach in 2009.


text:
\section{Introduction}

It is an interesting problem to determine the structure of rings of Siegel modular forms with respect to congruence subgroups. A famous theorem of Igusa \cite{I62} shows that every Siegel modular form of degree two and even weight for the full modular group $\mathrm{Sp}_4(\mathbb{Z})$ can be written uniquely as a polynomial in forms $\phi_4, \phi_6, \phi_{10}, \phi_{12}$ of weights $4, 6, 10, 12$, and that odd weight Siegel modular forms are precisely the products of even weight Siegel modular forms with a distinguished cusp form $\psi_{35}$ of weight $35$. It was proved by Aoki and Ibukiyama \cite{AI} that the rings of modular forms for the congruence subgroups $$\Gamma_{0, 1}^{(2)}(N) = \Big\{ \begin{psmallmatrix} a & b \\ c & d \end{psmallmatrix} \in \mathrm{Sp}_4(\mathbb{Z}): \; c \equiv 0 \, (N), \; \mathrm{det}(a) \equiv \mathrm{det}(d) \equiv 1 \, (N)\Big\}, \; N = 2, 3, 4$$ have an analogous structure: they are generated by four algebraic independent modular forms together with their Jacobian (or first Rankin--Cohen--Ibukiyama bracket). The rings $M_*(\Gamma_0^{(2)}(N))$ where $$\Gamma_0^{(2)}(N) = \{\begin{psmallmatrix} a & b \\ c & d \end{psmallmatrix}\in \mathrm{Sp}_4(\mathbb{Z}): \, c \equiv 0 \, (N)\}$$ therefore have a simple structure as well.

The goal in this paper is to extend the methods of Aoki and Ibukiyama to level $N=5$. This is not quite straightforward, as the natural underlying ring is no longer  $M_*(\Gamma_{0,1}^{(2)}(5))$ but rather a ring $M_*^!(\Gamma_{0,1}^{(2)}(5))$ of meromorphic Siegel modular forms with singularities on Humbert surfaces. We will define a hyperplane arrangement $\mathcal{H}$ as the $\Gamma_0^{(2)}(5)$-orbit of the Humbert surface $$\{Z = \begin{psmallmatrix} \tau & z \\ z & w \end{psmallmatrix} \in \mathbb{H}_2: \; \mathrm{det}(Z) = 1 - 5z\},$$
which, if one views points in $\mathbb{H}_2$ as parameterizing abelian surfaces, is a locus of principally polarized abelian surfaces with real multiplication that respects a $\Gamma_0^{(2)}(5)$ level structure. We then investigate the ring $M_*^!(\Gamma_{0, 1}^{(2)}(5))$ of meromorphic Siegel modular forms on $\Gamma_{0, 1}^{(2)}(5)$ with singularities supported on $\mathcal{H}$.    Using a generalization of the modular Jacobian approach of \cite{Wan21a}, we prove in Theorem \ref{th:singular1} that $M_*^!(\Gamma_{0, 1}^{(2)}(5))$ is generated by four algebraically independent singular additive lifts $f_1, f_2, g_1, g_2$ of weights $1$, $1$, $2$, $2$ and by their Jacobian; in particular, the associated threefold $X_{0, 1}^{(2)}(5)$ is rational.  The local isomorphism from $\mathrm{Sp}_4$ to $\mathrm{SO}(3,2)$ and Borcherds' theory of orthogonal modular forms with singularities are essential. $\mathrm{Proj}(M_*^!(\Gamma_{0, 1}^{(2)}(5)))$ is the Looijenga compactification \cite{Loo03b} of the complement $(\mathbb{H}_2 \setminus \mathcal{H}) / \Gamma_{0, 1}^{(2)}(5)$, which plays a similar role to the Satake--Baily--Borel compactification of $Y_{0,1}^{(2)}(5)$.

It follows from the above that every Siegel modular form of level $\Gamma_0^{(2)}(5)$ can be expressed uniquely in terms of the basic forms $f_1, f_2, g_1, g_2$. It is not clear to the authors how to compute the ring $M_*(\Gamma_0^{(2)}(5))$ of (holomorphic) Siegel modular forms from this information alone; however, allowing a formula of Hashimoto \cite{H} for the dimensions of cusp forms (itself an application of the Selberg trace formula), the ring structure becomes a straightforward Gr\"obner basis computation. We will prove that $M_*(\Gamma_0^{(2)}(5))$ is minimally generated by eighteen modular forms of weights $2, 4, 4, 4, 4, 4, 6, 6, 6, 6, 10, 11, 11, 11, 13, 13, 13, 15$ in Theorem \ref{thm:lvl5hol}.

This paper is organized as follows. In \S \ref{sec:pre} we review the realization of Siegel modular groups as orthogonal groups and the theory of Borcherds lifts. In \S \ref{sec:meromorphic} we determine two rings of meromorphic Siegel modular forms. In \S \ref{sec:holomorphic} we use this to determine the ring of holomorphic Siegel modular forms for $\Gamma_{0}^{(2)}(5)$.

\section{Theta lifts to Siegel modular forms of degree two}\label{sec:pre}

\subsection{$\Gamma_0^{(2)}(N)$ as an orthogonal group}
Recall that the Pfaffian of an antisymmetric $(4 \times 4)$-matrix $M$ is $$\mathrm{pf}(M) = \mathrm{pf}\begin{psmallmatrix} 0 & a & b & c \\ -a & 0 & d & e \\ -b & -d & 0 & f \\ -c & -e & -f & 0 \end{psmallmatrix} = af - be + cd.$$ We view $\mathrm{pf}$ as a quadratic form and define the associated bilinear form $$\langle x, y \rangle = \mathrm{pf}(x + y) - \mathrm{pf}(x) - \mathrm{pf}(y).$$ The Pfaffian is invariant under conjugation $M \mapsto A^T M A$ by $A \in \mathrm{SL}_4(\mathbb{R})$ and this action identifies $\mathrm{SL}_4(\mathbb{R})$ with the Spin group $\mathrm{Spin}(\mathrm{pf})$. The symplectic group $\mathrm{Sp}_4(\mathbb{R})$, by definition, preserves $$\mathcal{J} = \begin{psmallmatrix} 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{psmallmatrix}$$ under conjugation, so it also preserves the orthogonal complement $\mathcal{J}^{\perp}$; and indeed it is exactly the Spin group of $\mathrm{pf}$ restricted to $\mathcal{J}^{\perp}$. If the entries of $M$ are labelled as above then $M \in \mathcal{J}^{\perp}$ if and only if $b + e = 0$.

For any $N \in \mathbb{N}$, the group $\Gamma_0^{(2)}(N) = \{\begin{psmallmatrix} a & b \\ c & d \end{psmallmatrix} \in \mathrm{Sp}_4(\mathbb{Z}): \; c \equiv 0 \, (N)\}$ stabilizes the lattice $$L = \Big\{ M = \begin{psmallmatrix} 0 & a & b & c \\ -a & 0 & d & -b \\ -b & -d & 0 & f \\ -c & b & -f & 0 \end{psmallmatrix}: \; a, b, c, d, f \in \mathbb{Z}, \; a \equiv 0 \, (N)\Big\}$$ which is of type $U \oplus U(N) \oplus A_1$.
By \cite[\S 2]{HK} the special discriminant kernel $\widetilde{\mathrm{SO}}(L)$ of $L$ is exactly the projective modular group $\Gamma_{0, 1}^{(2)}(N) / \{\pm I\}$ under this identification, where
\begin{align*}
\widetilde{\mathrm{SO}}(L)&=\{ g \in \mathrm{SO}(L):\; g(v)-v\in L \; \text{for all}\; v \in L' \},\\
\Gamma_{0, 1}^{(2)}(N) &= \{\begin{psmallmatrix} a & b \\ c & d \end{psmallmatrix} \in \Gamma_0^{(2)}(N): \; \mathrm{det}(a) \equiv 1 \, (N)\}.
\end{align*}
It follows that $$\Gamma_0^{(2)}(N) / \{\pm I\} = \langle \widetilde{\mathrm{SO}}(L), \; \varepsilon_u: \; u \in (\mathbb{Z} / N\mathbb{Z})^{\times} \rangle$$ where $\varepsilon_u$ is the matrix $$\varepsilon_u = \begin{pmatrix} u & 0 & b & 0 \\ 0 & 1 & 0 & 0 \\ N & 0 & u^* & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} \in \Gamma_0^{(2)}(N)$$ for any integer solutions $u^*, b$ to $uu^* - Nb = 1$ (the choice does not matter). The map induced by $\varepsilon_u$ on $L'/L \cong A_1'/A_1 \oplus U(N)'/U(N)$ acts trivially on $A_1'/A_1$ and acts on $U(N)'/U(N) \cong \mathbb{Z}/N\mathbb{Z} \oplus \mathbb{Z}/N\mathbb{Z}$ as the map $$\varepsilon_u : \mathbb{Z}/N\mathbb{Z} \oplus \mathbb{Z}/N\mathbb{Z} \rightarrow \mathbb{Z}/N\mathbb{Z} \oplus \mathbb{Z}/N\mathbb{Z}, \; (x, y) \mapsto (ux, u^{-1}y).$$

The symplectic group $\mathrm{Sp}_4(\mathbb{R})$ acts on the Siegel upper half-space $\mathbb{H}_2$ by M\"obius transformations: $$M \cdot Z = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \cdot Z = (aZ + b)(cZ + d)^{-1}.$$ Let $j(M; Z) = \mathrm{det}(c Z + d)$ be the usual automorphy factor. We embed the Siegel upper half-space into $L \otimes \mathbb{C}$ as follows: $$Z = \begin{pmatrix} \tau & z \\ z & w \end{pmatrix} \mapsto \mathcal{Z} := \phi(Z) := \begin{pmatrix} 0 & 1 & z & w \\ -1 & 0 & -\tau & -z \\ -z & \tau & 0 & \tau w - z^2 \\ -w & z & z^2 - \tau w & 0 \end{pmatrix}.$$ Then one has the relation $$M^T \mathcal{Z} M = j(M; Z) \phi(M \cdot Z), \; M \in \mathrm{Sp}_4(\mathbb{R})$$ as one can check on any system of generators.

For any $\lambda \in L'$ of positive norm $D = Q(\lambda)$, the space $$\{Z \in \mathbb{H}_2: \; \mathcal{Z} \in \lambda^{\perp}\}$$ is known as a \textbf{Humbert surface} $H(D, \lambda)$ of discriminant $D$. If $\lambda$ is written in the form $\begin{psmallmatrix} 0 & a & b & c \\ -a & 0 & d & -b \\ -b & -d & 0 & f \\ -c & b & -f & 0 \end{psmallmatrix}$ then $$H(D, \lambda) = \{Z = \begin{psmallmatrix} \tau & z \\ z & w \end{psmallmatrix} \in \mathbb{H}_2: \; a \mathrm{det}(Z) -c \tau + 2bz + dw + f = 0 \}.$$ If $\gamma$ instead is a coset of $L'/L$, then we define $$H(D, \gamma) = \sum_{\substack{\lambda \in \gamma \\ \lambda \; \text{primitive in}\; L' \\ Q(\lambda) = D}} H(D, \lambda).$$ These unions are locally finite and therefore descend to well-defined divisors on $\widetilde{\mathrm{O}}(L) \backslash \mathbb{H}_2.$ We will use the notation $H(D, \pm \gamma)$ because $\lambda^{\perp} = (-\lambda)^{\perp}$ implies $H(D, \gamma) = H(D, -\gamma)$. Note that many references omit the condition that $\lambda$ be primitive in $L'$, so $H(D, \pm \gamma)$ satisfy inclusions; our divisors $H(D, \pm \gamma)$ do not.

\subsection{Theta lifts}
Let $L$ be the lattice in the space of $(4 \times 4)$ antisymmetric matrices from the previous subsection. The \textbf{weight $k$ theta kernel} is $$\Theta_k(\tau; Z) = \frac{\pi^k}{\mathrm{det}(V)^k \Gamma(k)} \sum_{\lambda \in L'} \langle \lambda, \mathcal{Z} \rangle^k e^{-\frac{\pi y}{\mathrm{det}(V)} | \langle \lambda, \mathcal{Z} \rangle|^2} e^{2\pi i \overline{\tau} \mathrm{pf}(\lambda)} \mathfrak{e}_{\lambda},$$ where $\tau = x+iy \in \mathbb{H}$; and $Z = U+iV \in \mathbb{H}_2$; and $\mathcal{Z}$ is the image of $Z$ in $L \otimes \mathbb{C}$. By applying a theorem of Vign\'eras on indefinite theta series \cite{V} one sees that $\Theta_k$ transforms like a modular form of weight $\kappa:= k -1/2$ with respect to the Weil representation $\rho_L$. On the other hand, for any $M = \begin{psmallmatrix} a & b \\ c & d \end{psmallmatrix} \in \Gamma_0^{(2)}(N)$,
\begin{align*} \Theta_k(\tau; M \cdot Z) &= \frac{\pi^k}{\mathrm{det} \, \mathrm{im}(M \cdot Z)^k \Gamma(k)} \sum_{\lambda \in L'} \mathrm{det}(cZ + d)^{-k} \langle \lambda, M^T \mathcal{Z} M \rangle e^{-\frac{\pi y}{\mathrm{det}(V)} | \langle \lambda, M^T \mathcal{Z} M \rangle|^2} e^{2\pi i \overline{\tau} \mathrm{pf}(\lambda)} \mathfrak{e}_{\lambda} \\ &= \frac{\pi^k}{\mathrm{det}(V)^k \Gamma(k)} \overline{\mathrm{det}(cZ + d)^k} \sum_{\lambda \in L'} \langle M^{-T} \lambda M^{-1}, \mathcal{Z} \rangle^k e^{-\frac{\pi y}{\mathrm{det}(V)} | \langle M^{-T} \lambda M^{-1},  \mathcal{Z} \rangle|^2} e^{2\pi i \overline{\tau} \mathrm{pf}(M^{-T} \lambda M^{-1})} \mathfrak{e}_{\lambda} \\ &= \overline{\mathrm{det}(cZ + d)^k} \sigma(M) \Theta_k(\tau; Z),   \end{align*} where $\sigma$ is the map $$\sigma : \Gamma_0^{(2)}(N) \longrightarrow \mathrm{Aut} \, \mathbb{C}[L'/L], \; \; \sigma(M) \mathfrak{e}_{\lambda} := \mathfrak{e}_{M^T \lambda M}.$$

Following Borcherds \cite{B} one defines the theta lift of a vector-valued modular form $F$ with a pole at $\infty$ as the regularized integral of $F$ against the kernel $\Theta_k$:

\begin{defn} (i) The \emph{Weil representation} $\rho_L$ associated to an even lattice $(L, Q)$ is the representation $\rho : \mathrm{Mp}_2(\mathbb{Z}) \rightarrow \mathrm{GL}\, \mathbb{C}[L'/L]$ defined by $$\rho\left( \begin{psmallmatrix} 1 & 1 \\ 0 & 1 \end{psmallmatrix}, 1 \right) \mathfrak{e}_{\gamma} = e^{-2\pi i Q(\gamma)}\mathfrak{e}_{\gamma};$$ $$\rho\left( \begin{psmallmatrix} 0 & -1 \\ 1 & 0 \end{psmallmatrix}, \sqrt{\tau} \right) \mathfrak{e}_{\gamma} = e^{\pi i \mathrm{sig}(L)/4} |L'/L|^{-1/2} \sum_{\beta \in L'/L} e^{2\pi i \langle \gamma, \beta \rangle} \mathfrak{e}_{\beta}.$$ Here $\mathrm{Mp}_2(\mathbb{Z})$ is the metaplectic group of pairs $(M, \phi)$ where $M = \begin{psmallmatrix} a & b \\ c & d \end{psmallmatrix} \in \mathrm{SL}_2(\mathbb{Z})$ and $\phi$ is a square root of $c\tau + d$, and $\mathfrak{e}_{\gamma}$, $\gamma \in L'/L$ is the standard basis of the group ring $\mathbb{C}[L'/L]$.\\
(ii) A \emph{nearly-holomorphic vector-valued modular form} for $\rho_L$ is a holomorphic function $F : \mathbb{H} \rightarrow \mathbb{C}[L'/L]$ which satisfies $$F((M, \phi) \cdot \tau) = \phi(\tau)^{2k} \rho_L(M) F(\tau), \; \; (M, \phi) \in \mathrm{Mp}_2(\mathbb{Z})$$ and which is meromorphic at the cusp $\infty$, i.e. its Fourier series has only finitely many negative exponents. \\
(iii) Let $k \ge 1$ and let $F \in M_{\kappa}^!(\rho_L)$ be a nearly-holomorphic modular form. The \textbf{(singular) theta lift} of $F$ is $$\Phi_F(Z) = \int^{\mathrm{reg}}_{\mathrm{SL}_2(\mathbb{Z}) \backslash \mathbb{H}} \langle F(\tau), \Theta_k(\tau; Z) \rangle y^{\kappa} \frac{\mathrm{d}x \, \mathrm{d}y}{y^2}.$$
\end{defn}

Here the regularization means one takes the limit as $w \rightarrow \infty$ of the integral over $\mathcal{F}_w = \{\tau = x+iy \in \mathbb{H}: \; x^2 + y^2 \ge 1, \; |x| \le 1/2, \; y \le w\}$; in effect, it means one integrates first with respect to $x$, which mollifies the contribution of the principal part of $F$ to the integral; and then secondly with respect to $y$. The behavior of the theta lift under M\"obius transformations is \begin{align*} \Phi_F(M \cdot Z) &= \int^{\mathrm{reg}} \langle F(\tau), \Theta_k(\tau; M \cdot Z) \rangle \; y^{\kappa - 2} \, \mathrm{d}x \, \mathrm{d}y \\ &= \mathrm{det}(cZ + d)^k \int^{\mathrm{reg}} \sum_{\gamma \in L'/L} F_{\gamma}(\tau) \overline{\Theta_{k; M^{-T} \gamma M^{-1}}(\tau; Z)} \, y^{\kappa - 2} \, \mathrm{d}x \, \mathrm{d}y \\ &= \mathrm{det}(cZ+d)^k \Phi_{\sigma(M)^{-1} F}(Z). \end{align*}
Therefore, the singular theta lift $\Phi_F$ defines a meromorphic Siegel modular form of weight $k$ on the subgroup of $\Gamma_0^{(2)}(N)$ that fixes $F$, with singularities of multiplicity $k$ along Humbert surfaces associated to the principal part of the input $F$. This is the so-called Borcherds additive lift. We refer to \cite[Theorem 14.3]{B} for more details. Since the Borcherds additive lift is a generalization of the Gritsenko lift \cite{G88}, we also call it the singular Gritsenko lift.  When the input $F$ has weight $\kappa=-\frac{1}{2}$ (i.e. $k=0$), the modified exponential of $\Phi_F$ defines a remarkable modular form which has an infinite product expansion (cf. \cite[Theorem 13.3]{B}), called a \emph{Borcherds product}, or more specifically the Borcherds lift of $F$. In this paper we will need both types of singular theta lifts.

\begin{rem} It is often useful to consider the \emph{pullback} or restriction of a Siegel modular form to a Humbert surface, the result being traditionally interpreted as a Hilbert modular form attached to a real-quadratic field. From the point of view of orthogonal modular forms this is very simple: to restrict a form $\Phi(Z)$ to the sublattice $v^{\perp}$ (with $v \in L'$) one simply restricts to $Z$ satisfying $\langle Z, v \rangle = 0$.

The pullback of a theta lift $\Phi_F$ as above is again a theta lift, $\Phi_{\vartheta F}$, where $\vartheta F \in M_{\kappa + 1/2}(\rho_{v^{\perp}})$ is the \emph{theta contraction}, obtained roughly by tensoring $F$ with a unary theta series and averaging out. The important point is that one can check rigorously whether a theta lift $\Phi_F$ vanishes identically on a Heegner divisor, with the computations taking place only on the level of vector-valued modular forms.
\end{rem}

\section{The ring of meromorphic Siegel modular forms of level 5}\label{sec:meromorphic}
We consider the ring $M_*^!(\Gamma_0^{(2)}(5))$ of meromorphic Siegel modular forms of level $\Gamma_0^{(2)}(5)$ whose poles may lie only on the orbit $\mathcal{H}$ of the Humbert surface $$\{Z = \begin{psmallmatrix} \tau & z \\ z & w \end{psmallmatrix} \in \mathbb{H}_2: \; \mathrm{det}(Z) = 1 - 5z\},$$ which is a locus of principally polarized RM abelian surfaces with $\Gamma_0^{(2)}(5)$ level structure. In view of our discussion earlier, $\mathcal{H}$ splits as the union of two irreducible $\Gamma_{0, 1}^{(2)}(5)$-orbits of Humbert surfaces: $$\mathcal{H} = H(1/20, \pm \gamma_1) + H(1/20, \pm \gamma_2),$$ each invariant under the discriminant kernel of $L = U\oplus U(5)\oplus A_1$, where we have fixed any coset $\gamma_1 \in L'/L$ of norm $1/20 + \mathbb{Z}$ and define $\gamma_2 = \varepsilon_2(\gamma_1)$. The Humbert surface $H_{1/5}$ of discriminant $1/5$, the orbit of $\{\begin{psmallmatrix} \tau & z \\ z & w \end{psmallmatrix} \in \mathbb{H}_2: \; \tau = 2z\}$ under $\Gamma_0^{(2)}(5)$, also splits into two $\Gamma_{0, 1}^{(2)}(5)$-invariant divisors: $$H_{1/5} = H(1/5, \pm \delta_1) + H(1/5, \pm \delta_2),$$ where $\delta_n = 2\gamma_n \in L'/L$.

For a finite-index subgroup $\Gamma \le \Gamma_0^{(2)}(5)$ or $\Gamma \le \mathrm{O}(L)$, we define $M_*^!(\Gamma,\chi)$ to be the ring of meromorphic forms, holomorphic away from $\mathcal{H}$, which are modular under $\Gamma$ with character $\chi$.

We first prove a form of Koecher's principle for meromorphic modular forms with poles supported on $\mathcal{H}$.

\begin{lem}\label{lem:Koecher}
Let $f\in M_k^!(\Gamma_{0,1}^{(2)}(5),\chi)$. If $k$ is negative, then $f$ is identically zero. If $k=0$, then $f$ is constant.
\end{lem}
\begin{proof}
We prove the lemma in the context of $\mathrm{O}(3, 2)$. Let $v$ and $u\neq \pm v$ be primitive vectors of norm $1/20$ in $L'$, such that $v^\perp, u^\perp \in \mathcal{H}$. Suppose that $f$ is not identically zero and has poles of multiplicity $c_v$ along $v^\perp$.  We denote the intersection of $v^\perp$ and the symmetric domain $\mathbb{H}_2$ (resp. the lattice $L$) by $v^\perp \cap \mathbb{H}_2$ (resp. $L_v$). Then $L_v$ is a lattice of signature $(2,2)$ and discriminant $5$, equivalent to the lattice $U + \mathbb{Z}[(1 + \sqrt{5}) / 2]$ where the quadratic form is the field norm. It is easy to see that the space $L_v\otimes \mathbb{Q}$ contains no isotropic planes, so the Koecher principle holds for modular forms on $\widetilde{\mathrm{O}}(L_v)$. We find that the projection of $u$ in $L_v$ has non-positive norm, which implies that the intersection of $u^\perp$ and $v^\perp \cap \mathbb{H}_2\cong \mathbb{H}\times \mathbb{H}$ is empty. Thus the quasi-pullback of $f$ to $v^\perp \cap \mathbb{H}_2$, i.e. the leading term in the power series expansion about that hyperplane, is a nonzero holomorphic modular form of weight $k-c_v$. By Koecher's principle we conclude $k-c_v\geq 0$ and therefore $k \ge 0$, and when $k=0$, we must have $c_v=0$ and thus $f$ is holomorphic and must be constant (by Koecher's principle on $\widetilde{\mathrm{O}}(L)$).
\end{proof}

We now construct some basic modular forms using Borcherds additive lifts (singular Gritsenko lifts) and Borcherds products.

\begin{lem}\label{wt1} There are singular Gritsenko lifts $f_1, f_2$ of weight one on $\widetilde{\mathrm{O}}(L)$ whose divisors are exactly $$\mathrm{div}(f_1) = -H(1/20, \pm \gamma_1) + 4H(1/20, \pm \gamma_2) + H(1/5, \pm \delta_1)$$ and $$\mathrm{div}(f_2) = 4H(1/20, \pm \gamma_1) - H(1/20, \pm \gamma_2) + H(1/5, \pm \delta_2).$$
\end{lem}
\begin{proof} Using the algorithm of \cite{W} we find a nearly-holomorphic modular form of weight $1/2$ for the Weil representation associated to $L$ whose Fourier expansion takes the form $$2 q^{-1/20}(\mathfrak{e}_{\gamma_1} - \mathfrak{e}_{-\gamma_1}) + O(q^{1/20}),$$ which is mapped under the Gritsenko lift to a meromorphic form $f_1$ with simple poles only on $H(1/20, \pm \gamma_1)$ and $H(1/20, \pm \gamma_4)$. Applying the automorphism $\varepsilon_2$ on $L'/L$ to the input into $f_1$ yields the input into $f_2$.

On the other hand, we found a nearly-holomorphic modular form of weight $-1/2$ whose principal part at $\infty$ is $$2 \mathfrak{e}_0 - 2q^{-1/20} (\mathfrak{e}_{\gamma_1} + \mathfrak{e}_{-\gamma_1}) + 4q^{-1/20} (\mathfrak{e}_{\gamma_2} + \mathfrak{e}_{-\gamma_2}) + q^{-1/5} (\mathfrak{e}_{\delta_1} + \mathfrak{e}_{-\delta_1}),$$ which is mapped under the Borcherds lift to a meromorphic modular form $F_1$ (possibly with character) of weight one and the claimed divisor. By taking theta contractions of the input form one finds that $f_1$ vanishes on $H(1/5, \pm \delta_1)$. Then the quotient $f_1 / F_1$ lies in $M_0^!(\widetilde{\mathrm{O}}(L), \chi)$ so it is constant by Lemma \ref{lem:Koecher}.
\end{proof}

\begin{rem} The Fourier expansions of $f_1$ and $f_2$ begin
\begin{align*}
f_1 \left( \begin{psmallmatrix} \tau & z \\ z & w \end{psmallmatrix}\right) &= 1 + 3q + 3s + 4q^2 + (2r^{-1} + 6 + 2r) qs + 4s^2 + O(q,s)^3;\\
f_2 \left( \begin{psmallmatrix} \tau & z \\ z & w \end{psmallmatrix} \right) &= q - s - 2q^2 + 2s^2 + 4q^3 + (4r^2 + 2 + 4r) qs (q - s) - 4s^3 + O(q, s)^4;
\end{align*}
where as usual $q = e^{2\pi i \tau}$, $r = e^{2\pi i z}$, $s = e^{2\pi i w}$. For more coefficients see Figure \ref{tab:coeffs} below. Setting $s = 0$ one obtains the (holomorphic) modular forms $$\Phi(f_1) = 1 + 3q + 4q^2 \pm ..., \; \Phi(f_2) = q - 2q^2 + 4q^3 \pm ...$$ of weight one and level $\Gamma_1(5)$ which freely generate the ring $M_*(\Gamma_1(5))$.
\end{rem}

There are nine Heegner divisors of discriminant $1/4$. One is the mirror of the reflective vector $r = 1/2 \in A_1'$, represented by the diagonal in $\mathbb{H}_2$, and the other eight are of the form $H(1/4, r + \gamma)$ where $\gamma$ are the isotropic cosets of $U(5)'/U(5)$. It will be convenient to fix concrete representatives. We take the Gram matrix $\mathbf{S} = \begin{psmallmatrix} 0 & 0 & 5 \\ 0 & 2 & 0 \\ 5 & 0 & 0 \end{psmallmatrix}$ for $U(5) \oplus A_1$, such that $L'/L \cong \mathbf{S}^{-1} \mathbb{Z}^3 / \mathbb{Z}^3$ and fix the cosets \begin{align*} &\gamma_1 = (1/5, 1/2, 4/5) + L&  &\gamma_2 = (2/5, 1/2, 2/5) + L& \\ &\gamma_3 = (3/5, 1/2, 3/5) + L&  &\gamma_4 = (4/5, 1/2, 1/5) + L&\end{align*} of norm $1/20 + \mathbb{Z}$. The norm $1/4$ cosets other than $r$ are labelled $$\alpha_n = (n/5, 1/2, 0) + L, \; \beta_n = (0, 1/2, n/5) + L, \; n \in \{1, 2, 3, 4\}.$$

\begin{lem} There are singular Gritsenko lifts $g_1, g_2, h_1, h_2$ of weight two on $\widetilde{\mathrm{O}}(L)$ whose divisors are exactly \begin{align*} \mathrm{div}\, g_1 &= 3 H(1/20, \pm \gamma_1) - 2 H(1/20, \pm \gamma_2) + H(1/4, \pm \alpha_2); \\ \mathrm{div}\, g_2 &= -2H(1/20, \pm \gamma_1) + 3H(1/20, \pm \gamma_2) + H(1/4, \pm \alpha_1); \\ \mathrm{div}\, h_1 &= 3 H(1/20, \pm \gamma_1) - 2 H(1/20, \pm \gamma_2)+ H(1/4, \pm \beta_2); \\ \mathrm{div}\, h_2 &= -2H(1/20, \pm \gamma_1) + 3H(1/20, \pm \gamma_2) + H(1/4, \pm \beta_1). \end{align*}
\end{lem}
\begin{proof} The proof is essentially the same argument as Lemma \ref{wt1}. Using the pullback trick, one constructs weight two Gritsenko lifts which vanish on the claimed discriminant $1/4$ Heegner divisors. Then one constructs Borcherds products of weight two with the claimed divisors. The respective quotients lie in $M_0^!(\widetilde{\mathrm{O}}(L), \chi)$ and are therefore constant by Lemma \ref{lem:Koecher}. To determine the precise (nearly-holomorphic) vector-valued modular forms which lift to $g_1, g_2, h_1, h_2$, one only needs to compute the four-dimensional space of nearly-holomorphic forms of weight $3/2$ for $\rho_L$ with a pole of order at most $1/20$ at $\infty$, and identify the unique (up to scalar) forms whose pullback to $\alpha_n^{\perp}$ or $\beta_n^{\perp}$ is respectively zero. The input forms $G_1, G_2, H_1, H_2$ can be chosen such that their Fourier expansions begin as follows: \begin{align*} G_1: &\quad q^{-1/20} (\mathfrak{e}_{\gamma_2} + \mathfrak{e}_{\gamma_3}) +  (\mathfrak{e}_{(0, 0, 1/5)} + \mathfrak{e}_{(0, 0, 4/5)} - \mathfrak{e}_{(0, 0, 2/5)} + \mathfrak{e}_{(0, 0, 3/5)} ) + O(q^{1/20}) \\ G_2: &\quad q^{-1/20} (\mathfrak{e}_{\gamma_1} + \mathfrak{e}_{\gamma_4}) + (\mathfrak{e}_{(0, 0, 2/5)} + \mathfrak{e}_{(0, 0, 3/5)} - \mathfrak{e}_{(0, 0, 1/5)} + \mathfrak{e}_{(0, 0, 4/5)} ) + O(q^{1/20}) \\ H_1: &\quad q^{-1/20} (\mathfrak{e}_{\gamma_2} + \mathfrak{e}_{\gamma_3}) + (\mathfrak{e}_{(1/5, 0, 0)} + \mathfrak{e}_{(4/5, 0, 0)} - \mathfrak{e}_{(2/5, 0, 0)} + \mathfrak{e}_{(3/5, 0, 0)} ) + O(q^{1/20}) \\ H_2: &\quad q^{-1/20} (\mathfrak{e}_{\gamma_1} + \mathfrak{e}_{\gamma_4}) + (\mathfrak{e}_{(2/5, 0, 0)} + \mathfrak{e}_{(3/5, 0, 0)} - \mathfrak{e}_{(1/5, 0, 0)} + \mathfrak{e}_{(4/5, 0, 0)} )  + O(q^{1/20}). \end{align*} These expansions determine $G_1,G_2,H_1,H_2$ uniquely because there are no vector-valued cusp forms of weight $3/2$ for $\rho_L$.
\end{proof}

\begin{rem} The Fourier expansions of $g_1, g_2, h_1, h_2$ begin as follows:
\begin{align*}
g_1\left( \begin{psmallmatrix} \tau & z \\ z & w \end{psmallmatrix}\right) &= q + q^2 - 5qs + 2q^3 + (-3r^{-1} + 1 - 3r) q^2 s + (-r^{-1} + 7 - r) qs^2 + O(q, s)^4;\\
g_2\left( \begin{psmallmatrix} \tau & z \\ z & w \end{psmallmatrix}\right) &= -q - q^2 + (r^{-1} + 3 + r)qs - 2q^3 + (-r^{-1} + 7 - r) q^2 s + (-3r^{-1} + 1 - 3r) qs^2 + O(q, s)^4;\\
h_1 \left( \begin{psmallmatrix} \tau & z \\ z & w \end{psmallmatrix}\right) &= s - 5qs + s^2 + (-r^{-1} +7 - r) q^2 s + (-3r^{-1} + 1 - 3r) qs^2 + 2s^3 + O(q, s)^4;\\
h_2 \left( \begin{psmallmatrix} \tau & z \\ z & w \end{psmallmatrix}\right) &= -s + (r^{-1} + 3 + r) qs - s^3 + (-3r^{-1} + 1 - 3r) q^2 s + (-r^{-1} + 7 - r) qs^2 - 2s^3 + O(q, s)^4.
\end{align*}
\end{rem}

We can now determine the structure of $M_*^!(\Gamma_{0, 1}^{(2)}(5))$. Recall that $\Gamma_{0, 1}^{(2)}(5) /\{\pm I\} \cong \widetilde{\mathrm{SO}}(L)$. The decomposition
$$
M_k^!(\widetilde{\mathrm{SO}}(L))= M_k^!(\widetilde{\mathrm{O}}(L)) \oplus M_k^!(\widetilde{\mathrm{O}}(L), \det),
$$
suggests that we first consider the ring of modular forms for the discriminant kernel $\widetilde{\mathrm{O}}(L)$. We will show that $M_*^!(\widetilde{\mathrm{O}}(L))$ is freely generated using a generalization of the modular Jacobian approach of \cite[Theorem 5.1]{Wan21a}. We briefly introduce the main objects of this approach. For any four $\psi_i\in M_{k_i}^!(\widetilde{\mathrm{O}}(L))$ with $1\leq i\leq 4$, their Jacobian (see \cite[Theorem 2.5]{Wan21a} and \cite[Proposition 2.1]{AI})
\begin{equation*}
J(\psi_1,\psi_2,\psi_3,\psi_4)=\left\lvert \begin{array}{cccc}
k_1\psi_1 & k_2\psi_2 & k_3\psi_3 & k_4\psi_4 \\
[1mm]
\frac{\partial \psi_1}{\partial \tau} & \frac{\partial \psi_2}{\partial \tau} & \frac{\partial \psi_3}{\partial \tau} & \frac{\partial \psi_4}{\partial \tau} \\[1mm]
\frac{\partial \psi_1}{\partial z} & \frac{\partial \psi_2}{\partial z} & \frac{\partial \psi_3}{\partial z} & \frac{\partial \psi_4}{\partial z} \\
[1mm]
\frac{\partial \psi_1}{\partial w} & \frac{\partial \psi_2}{\partial w} & \frac{\partial \psi_3}{\partial w} & \frac{\partial \psi_4}{\partial w}
\end{array}   \right\rvert
\end{equation*}
lies in  $M_{k_1+k_2+k_3+k_4+3}^!(\widetilde{\mathrm{O}}(L),\det)$. The Jacobian $J(\psi_1,\psi_2,\psi_3,\psi_4)$ is not identically zero if and only if the four forms $\psi_i$ are algebraically independent over $\mathbb{C}$.

The discriminant kernel $\widetilde{\mathrm{O}}(L)$ contains reflections associated to vectors of norm 1 in $L$ (the so-called $2$-reflections)
$$
\sigma_v: x \mapsto x - (x,v)v.
$$
The hyperplane $v^\perp$ is called the mirror of the reflection $\sigma_v$. Since $\det(\sigma_v)=-1$, the chain rule implies that the above Jacobian vanishes on all mirrors of $2$-reflections. Conversely, the main theorem of \cite{Wan21a}, and its generalization to meromorphic modular forms with constrained poles, implies that

\begin{thm}\label{th:singular1}
The ring $M_*^!(\widetilde{\mathrm{O}}(L))$ is a free algebra: $$M_*^!(\widetilde{\mathrm{O}}(L)) = \mathbb{C}[f_1, f_2, g_1, g_2].$$
Define $J:=J(f_1,f_2,g_1,g_2)$. Then
$$
M_*^!(\Gamma_{0, 1}^{(2)}(5)) = \mathbb{C}[f_1, f_2, g_1, g_2, J].
$$
\end{thm}
\begin{proof} The Jacobian $J$ of $f_1, f_2, g_1, g_2$ has weight $9$ and vanishes on the mirrors of $2$-reflections, which form a union of Heegner divisors of discriminants $1/4$ and $1$ denoted $\Delta$. Using the Fourier expansions of the forms it is easy to check that $J$ is not identically zero. Using the algorithm of \cite{W} we find a Borcherds product $J_0$ with divisor $$\mathrm{div}\, J_0 = \Delta + 6 H(1/20, \pm \gamma_1) + 6 H(1/20, \pm \gamma_2).$$ The quotient $J / J_0$ lies in $M_0^!(\Gamma_{0, 1}^{(2)}(5),\chi)$ and is therefore a constant denoted $c$ by Lemma \ref{lem:Koecher}. We will now prove the claim by an argument which appeared essentially in \cite{Wan21a}. Suppose that $M_*^!(\widetilde{\mathrm{O}}(L))$ was not generated by $h_1 := f_1$, $h_2 := f_2$, $h_3 := g_1$ and $h_4 := g_2$, and let $h_5 \in M_{k_5}^!(\widetilde{\mathrm{O}}(L))$ be a modular form of minimal weight which is not contained in $\mathbb{C}[f_1,f_2,g_1,g_2]$. Set $k_1 = k_2 = 1$ and $k_3 = k_4 = 2$, such that $k_i$ is the weight of $h_i$. For $1\leq j \leq 5$ we define $J_j$ as the Jacobian of the four modular forms $h_i$ omitting $h_j$, such that $c J_0=J=J_{5}$.  It is clear that $g_j:=J_j/J$ is a modular form on $\widetilde{\mathrm{O}}(L)$ with poles supported on $\mathcal{H}$. We compute the determinant and find the identity
$$
0 = \mathrm{det} \begin{pmatrix} k_1 h_1 & ... & k_4 h_4 & k_5 h_5 \\ k_1 h_1 & ... & k_4 h_4 & k_5 h_5 \\ \nabla h_1 & ... & \nabla h_4 & \nabla h_5 \end{pmatrix} = \sum_{i=1}^5 (-1)^{i+1} k_i h_i J_i.
$$
Since $J_i=Jg_i$ and $g_5=1$, we have
$$
\sum_{i=1}^{5} (-1)^{i+1} k_t h_t g_t = 0, \quad  \text{i.e} \quad k_5 h_5 = \sum_{i=1}^4 (-1)^i h_i g_i.
$$
Since $h_5$ was chosen to have minimal weight, $g_i \in \mathbb{C}[h_1,h_2,h_3,h_4]$ for all $i$, and thus $h_5\in \mathbb{C}[h_1,h_2,h_3,h_4]$, which is a contradiction.

Now any $h\in M_k^!(\widetilde{\mathrm{O}}(L),\det)$ vanishes on all mirrors of $2$-reflections, which implies that $h/J \in M_{k-9}^!(\widetilde{\mathrm{O}}(L))$. Therefore $$M_*^!(\Gamma_{0,1}^{(2)}(5)) = M_*^!(\widetilde{\mathrm{SO}}(L)) = M_*^!(\widetilde{\mathrm{O}}(L)) \oplus M_*^!(\widetilde{\mathrm{O}}(L), \det)$$ is generated by $f_1$, $f_2$, $g_1$, $g_2$ and $J$.
\end{proof}

\begin{rem}
The weight two singular Gritsenko lifts satisfy the relations $$g_1 - h_1 = h_2 - g_2 = f_1 f_2.$$
The product $f_1 f_2$ is holomorphic and in fact itself a Gritsenko lift; but it has a quadratic character under $\Gamma_0^{(2)}(5)$. There is a unique normalized Siegel modular form $e_2$ of weight two for $\Gamma_0^{(2)}(5)$, which can be constructed as the Gritsenko lift of the unique vector-valued modular form of weight $3/2$ for $\rho_L$ invariant under all automorphisms of the discriminant form. (The uniqueness follows from Corollary \ref{cor:level5gen} blow.) In terms of the generators of $M_*^!(\Gamma_{0, 1}^{(2)}(5))$, a computation shows $$e_2 = f_1^2 + f_2^2 - 4(g_1 + g_2).$$
\end{rem}

\begin{cor}\label{cor:level5gen} The ring $M_*^!(\Gamma_0^{(2)}(5))$ is minimally generated in weights $2, 2, 4, 4, 4, 4, 4, 11, 11, 11$ by the ten forms
\begin{align*}
&f_1^2 + f_2^2,& &e_2,& &f_1^2 g_1 + f_2^2 g_2,& &f_1 f_2 (g_1 - g_2),& &f_1 f_2 (f_1 - f_2)(f_1 + f_2),&\\
&f_1^2 f_2^2,& &g_1 g_2,& &J f_1 f_2,& &J (f_1^2 - f_2^2),& &J (g_1 - g_2).&
\end{align*}
\end{cor}
\begin{proof} The group $\Gamma_0^{(2)}(5)$ is generated by the special discriminant kernel of $L$ and by the order four automorphism $\varepsilon_2$ which acts on the generators of $M_*^!(\Gamma_{0, 1}^{(2)}(5))$ by $$\varepsilon_2 : f_1 \mapsto f_2, \; f_2 \mapsto -f_1, \; g_1 \mapsto g_2, \; g_2 \mapsto g_1, \; J \mapsto -J$$ as one can see on the input functions into the Gritsenko lifts. We conclude the action of $\varepsilon_2$ on $J$ (as a Jacobian) from the actions of $\varepsilon_2$ on $f_1$, $f_2$, $g_1$ and $g_2$. The expressions in $f_1, f_2, g_1, g_2, J$ in the claim generate the ring of invariants under this action.
\end{proof}

\begin{rem} The same argument shows that the kernel of $\varepsilon_2^2 = \varepsilon_4$ is generated by $J$ and by the weight two forms $$f_1^2, f_2^2, f_1 f_2, g_1, g_2.$$ This corresponds to the quadratic Nebentypus $\chi\left( \begin{psmallmatrix} a & b \\ c & d \end{psmallmatrix} \right) = \left( \frac{5}{\mathrm{det}\, d}\right)$ on $\Gamma_0^{(2)}(5)$. Note that $f_1 f_2$ is the Siegel Eisenstein series of weight two for the character $\chi$, and that the Jacobian $J$ is the unique cusp form of weight nine for $\chi$ up to scalars.
\end{rem}

\begin{rem}\label{rem:liftslevel5} There is a seven-dimensional space of modular forms of weight $7/2$ for $\rho_L$, and a four-dimensional subspace on which $\varepsilon_2$ acts trivially, so the weight four Maass space for $\Gamma_0^{(2)}(5)$ is four-dimensional. Using the structure theorem above we can identify it by comparing only a few Fourier coefficients: $$\mathrm{Maass}_4 = \mathrm{Span}(\phi_1, \phi_2, \phi_3, \phi_4)$$ where \begin{align*} \phi_1 &= e_2^2 + f_1^2 f_2^2; \\ \phi_2 &= f_1^2 g_1 + f_2^2 g_2 - 2g_1 g_2; \\ \phi_3 &= f_1 f_2 (f_1^2 - 2 f_1 f_2 - f_2^2 + 2 g_1 - 2g_2); \\ \phi_4 &= 2 g_1 g_2 + f_1 f_2 (g_1 - g_2). \end{align*} The form $\phi_4$ is a cusp form and indeed spans $S_4(\Gamma_0^{(2)}(5))$, which was shown to be one-dimensional by Poor and Yuen \cite{PY}.
\end{rem}

\section{The ring of holomorphic Siegel modular forms of level 5}\label{sec:holomorphic}
In this section we investigate the ring $M_*(\Gamma_0^{(2)}(5))$ of holomorphic Siegel modular forms for $\Gamma_0^{(2)}(5)$. We will need the Hilbert--Poincar\'e series for this ring, which can be derived from dimension formulas available in the literature.
\begin{thm}\label{thm:dim} The Hilbert--Poincar\'e series of dimensions of modular forms for $\Gamma_0^{(2)}(5)$ is $$\sum_{k = 0}^{\infty} \mathrm{dim}\, M_k(\Gamma_0^{(2)}(5)) t^k = \frac{(1 - t)^2 (1 + t^7) P(t)}{(1 - t^2)^2 (1 - t^3)(1 - t^4)^2 (1 - t^5)}$$ where $P(t)$ is the irreducible palindromic polynomial $$P(t) = 1 + 2 t + 2 t^{2} +  t^{3} + 3 t^{4} + 5 t^{5} + 8 t^{6} + 8 t^{7} + 8 t^{8} + 5 t^{9} + 3 t^{10} +  t^{11} + 2 t^{12} + 2 t^{13} +  t^{14}.$$
\end{thm}
The first values of $\dim M_k(\Gamma_0^{(2)}(5))$ are given in Table \ref{tab} below.

\begin{table}[ht]
\caption{$\dim M_k(\Gamma_0^{(2)}(5))$}\label{tab}
\renewcommand\arraystretch{1.5}
\noindent\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
k & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 &15 & 16 &17 &18 & 19 \\
\hline
\text{dim} & 0 & 1 & 0 & 6 & 0 & 10 & 0 & 22 & 0 & 34 & 3 & 57 & 6 & 79 & 16 & 117 & 25 & 153 & 45  \\
\hline
\end{array}
\]
\end{table}

\begin{proof} The dimensions of the spaces of cusp forms of weight $k \ge 5$ have been computed in closed form by Hashimoto by means of the Selberg trace formula and in lower weights by Poor and Yuen \cite{PY}: we have $\mathrm{dim}\, S_4(\Gamma_0^{(2)}(5)) = 1$ and $\mathrm{dim}\, S_k(\Gamma_0^{(2)}(5)) = 0$ for $k \le 3$. All odd-weight modular forms are cusp forms, and by a more general theorem of B\"ocherer--Ibukiyama \cite{BI}, for even $k > 2$, $$\mathrm{dim}\, M_k(\Gamma_0^{(2)}(5)) = \mathrm{dim}\, S_k(\Gamma_0^{(2)}(5)) + 2 \cdot \mathrm{dim}\, S_k(\Gamma_0(5)) + 3.$$
\end{proof}
We can now determine the generators of $M_*(\Gamma_0^{(2)}(5))$ using Corollary \ref{cor:level5gen} together with the above generating series.

\begin{thm}\label{thm:lvl5hol} The ring of Siegel modular forms of level $\Gamma_0^{(2)}(5)$ is minimally generated by the weight two form $$e_2 = f_1^2 + f_2^2 - 4 g_1 - 4g_2,$$ five weight four forms $$f_1^2 g_1 + f_2^2 g_2, \quad f_1 f_2 (g_1 - g_2), \quad f_1 f_2 (f_1^2 - f_2^2), \quad f_1^2 f_2^2, \quad g_1 g_2,$$ four weight six forms $$f_1^2 f_2^2 (g_1 + g_2), \quad f_1^3 f_2 g_1 - f_2^3 f_1 g_2, \quad f_1^2 g_1^2 + f_2^2 g_2^2, \quad g_1 g_2 (f_1^2 + f_2^2),$$ the weight ten form $$f_1^2 f_2^2 (f_1^2 + f_2^2)^3,$$ three weight eleven forms $$f_1 f_2 J, \quad (f_1^2 - f_2^2) J, \quad  (g_1 - g_2) J,$$ three weight thirteen forms $$(f_1^2 + f_2^2) f_1 f_2 J, \quad (f_1^4 - f_2^4) J, \quad (f_1^2 + f_2^2)(g_1 - g_2) J,$$ and the weight fifteen form $$(f_1^2 - f_2^2)^3 J.$$
\end{thm}
\begin{proof} From the divisors of $f_1, f_2, g_1, g_2$ and $J$, it is easy to see that all of the forms above (except for $e_2$, which was discussed in the previous section) are holomorphic and $\varepsilon_2$-invariant. The Hilbert series of this ring was computed in Macaulay2 \cite{M2} and coincides exactly with the series predicted by Theorem \ref{thm:dim}, so we can conclude that these forms are sufficient to generate all holomorphic Siegel modular forms.
\end{proof}

\bigskip

\noindent
\textbf{Acknowledgements}
H. Wang was supported by the Institute for Basic Science (IBS-R003-D1).

\section{Appendix}

On the following pages, we list more Fourier coefficients of the basic meromorphic forms $f_1, f_2, g_1, g_2$, as well as the unique expression for $J^2$ as a polynomial in these forms.

Note that the polynomial representing $J^2$ must split into two irreducible factors, corresponding to the two classes of reflections whose mirrors lie in the divisor of $J$. One of these factors is $g_1 + g_2$.

\begin{figure}
    \centering

    \begin{tabular}{m|m|m||m|m|m|m}
        a & b & c & f_1 & f_2 & g_1 & g_2  \\ \hline
        0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 3 & 1 & 1 & -1 \\0 & 0 & 1 & 3 & -1 & 0 & 0 \\2 & 0 & 0 & 4 & -2 & 1 & -1 \\1 & -1 & 1 & 2 & 0 & 0 & 1 \\1 & 0 & 1 & 6 & 0 & -5 & 3 \\1 & 1 & 1 & 2 & 0 & 0 & 1 \\0 & 0 & 2 & 4 & 2 & 0 & 0 \\3 & 0 & 0 & 2 & 4 & 2 & -2 \\2 & -1 & 1 & 4 & -4 & -3 & -1 \\2 & 0 & 1 & 2 & -2 & 1 & 7 \\2 & 1 & 1 & 4 & -4 & -3 & -1 \\1 & -1 & 2 & 4 & 4 & -1 & -3 \\1 & 0 & 2 & 2 & 2 & 7 & 1 \\1 & 1 & 2 & 4 & 4 & -1 & -3 \\0 & 0 & 3 & 2 & -4 & 0 & 0 \\4 & 0 & 0 & 1 & -3 & 3 & -3 \\3 & -1 & 1 & 6 & 6 & -2 & 4 \\3 & 0 & 1 & -2 & -2 & -6 & 2 \\3 & 1 & 1 & 6 & 6 & -2 & 4 \\2 & -2 & 2 & 2 & 0 & 0 & 2 \\2 & -1 & 2 & 8 & 0 & 10 & -2 \\2 & 0 & 2 & 0 & 0 & -15 & -5 \\2 & 1 & 2 & 8 & 0 & 10 & -2 \\2 & 2 & 2 & 2 & 0 & 0 & 2 \\1 & -1 & 3 & 6 & -6 & 4 & -2 \\1 & 0 & 3 & -2 & 2 & 2 & -6 \\1 & 1 & 3 & 6 & -6 & 4 & -2 \\0 & 0 & 4 & 1 & 3 & 0 & 0 \\5 & 0 & 0 & 3 & 1 & 5 & -5 \\4 & -1 & 1 & 0 & -8 & -2 & 10 \\4 & 0 & 1 & 0 & 6 & -11 & -5 \\4 & 1 & 1 & 0 & -8 & -2 & 10 \\3 & -2 & 2 & 0 & 6 & 3 & -5 \\3 & -1 & 2 & 0 & 0 & -10 & 10 \\3 & 0 & 2 & 0 & 8 & 24 & -20 \\3 & 1 & 2 & 0 & 0 & -10 & 10 \\3 & 2 & 2 & 0 & 6 & 3 & -5 \\2 & -2 & 3 & 0 & -6 & 3 & -5 \\2 & -1 & 3 & 0 & 0 & -10 & 10 \\2 & 0 & 3 & 0 & -8 & 24 & -20 \\2 & 1 & 3 & 0 & 0 & -10 & 10 \\2 & 2 & 3 & 0 & -6 & 3 & -5 \\1 & -1 & 4 & 0 & 8 & -2 & 10 \\1 & 0 & 4 & 0 & -6 & -11 & -5 \\1 & 1 & 4 & 0 & 8 & -2 & 10 \\0 & 0 & 5 & 3 & -1 & 0 & 0 \\ 6 & 0 & 0 & 6 & 2 & 2 & -2 \\5 & -2 & 1 & 3 & -1 & 0 & 0 \\5 & -1 & 1 & -2 & 4 & -15 & 10 \\5 & 0 & 1 & 8 & -6 & 5 & 5 \\5 & 1 & 1 & -2 & 4 & -15 & 10 \\5 & 2 & 1 & 3 & -1 & 0 & 0 \\4 & -2 & 2 & 6 & -6 & -4 & -8 \\4 & -1 & 2 & -8 & 8 & 12 & 4 \\4 & 0 & 2 & 14 & -14 & -1 & -7
    \end{tabular}
    \quad
    \begin{tabular}{m|m|m||m|m|m|m}
        a & b & c & f_1 & f_2 & g_1 & g_2 \\ \hline
        4 & 1 & 2 & -8 & 8 & 12 & 4 \\ 4 & 2 & 2 & 6 & -6 & -4 & -8 \\ 3 & -3 & 3 & 2 & 0 & 0 & 3 \\3 & -2 & 3 & 6 & 0 & -5 & -11 \\3 & -1 & 3 & -6 & 0 & 40 & 1 \\3 & 0 & 3 & 16 & 0 & -50 & -6 \\3 & 1 & 3 & -6 & 0 & 40 & 1 \\3 & 2 & 3 & 6 & 0 & -5 & -11 \\3 & 3 & 3 & 2 & 0 & 0 & 3 \\2 & -2 & 4 & 6 & 6 & -8 & -4 \\2 & -1 & 4 & -8 & -8 & 4 & 12 \\2 & 0 & 4 & 14 & 14 & -7 & -1 \\2 & 1 & 4 & -8 & -8 & 4 & 12 \\2 & 2 & 4 & 6 & 6 & -8 & -4 \\1 & -2 & 5 & 3 & 1 & 1 & -1 \\1 & -1 & 5 & -2 & -4 & -9 & 4 \\1 & 0 & 5 & 8 & 6 & 11 & -1 \\1 & 1 & 5 & -2 & -4 & -9 & 4 \\1 & 2 & 5 & 3 & 1 & 1 & -1 \\0 & 0 & 6 & 6 & -2 & 0 & 0 \\7 & 0 & 0 & 4 & -2 & 6 & -6 \\6 & -2 & 1 & 6 & 0 & -5 & 3 \\6 & -1 & 1 & 0 & 0 & 10 & -10 \\6 & 0 & 1 & 8 & 0 & -20 & 24 \\6 & 1 & 1 & 0 & 0 & 10 & -10 \\6 & 2 & 1 & 6 & 0 & -5 & 3 \\5 & -2 & 2 & 6 & 8 & 5 & 5 \\5 & -1 & 2 & -4 & -12 & 15 & -35 \\5 & 0 & 2 & 6 & 18 & -15 & 35 \\5 & 1 & 2 & -4 & -12 & 15 & -35 \\5 & 2 & 2 & 6 & 8 & 5 & 5 \\4 & -3 & 3 & -4 & -4 & -1 & -3 \\4 & -2 & 3 & 6 & 6 & 24 & 12 \\4 & -1 & 3 & -12 & -12 & -43 & -49 \\4 & 0 & 3 & 10 & 10 & 70 & 50 \\4 & 1 & 3 & -12 & -12 & -43 & -49 \\4 & 2 & 3 & 6 & 6 & 24 & 12 \\4 & 3 & 3 & -4 & -4 & -1 & -3 \\3 & -3 & 4 & -4 & 4 & -3 & -1 \\3 & -2 & 4 & 6 & -6 & 12 & 24 \\3 & -1 & 4 & -12 & 12 & -49 & -43 \\3 & 0 & 4 & 10 & -10 & 50 & 70 \\3 & 1 & 4 & -12 & 12 & -49 & -43 \\3 & 2 & 4 & 6 & -6 & 12 & 24 \\3 & 3 & 4 & -4 & 4 & -3 & -1 \\2 & -2 & 5 & 6 & -8 & -1 & 11 \\2 & -1 & 5 & -4 & 12 & 9 & -29 \\2 & 0 & 5 & 6 & -18 & -21 & 41 \\2 & 1 & 5 & -4 & 12 & 9 & -29 \\2 & 2 & 5 & 6 & -8 & -1 & 11 \\1 & -2 & 6 & 6 & 0 & -5 & 3 \\1 & -1 & 6 & 0 & 0 & 10 & -10 \\1 & 0 & 6 & 8 & 0 & -20 & 24 \\1 & 1 & 6 & 0 & 0 & 10 & -10 \\1 & 2 & 6 & 6 & 0 & -5 & 3 \\0 & 0 & 7 & 4 & 2 & 0 & 0
    \end{tabular}
    \caption{Fourier coefficients of $\begin{psmallmatrix} a & b/2 \\ b/2 & c \end{psmallmatrix}$ in the basic forms $f_1, f_2, g_1, g_2$, $a + c \le 7$}
    \label{tab:coeffs}
\end{figure}
\clearpage
\begin{figure}
    \begin{align*} &J^2 = \\
& f_{1}^{8} f_{2}^{2} g_{1}^{4} + 22 f_{1}^{7} f_{2}^{3} g_{1}^{4} + 119 f_{1}^{6} f_{2}^{4} g_{1}^{4} - 22 f_{1}^{5} f_{2}^{5} g_{1}^{4} + f_{1}^{4} f_{2}^{6} g_{1}^{4} + 2 f_{1}^{8} f_{2}^{2} g_{1}^{3} g_{2} + 46 f_{1}^{7} f_{2}^{3} g_{1}^{3} g_{2} + 282 f_{1}^{6} f_{2}^{4} g_{1}^{3} g_{2} \\
& + 194 f_{1}^{5} f_{2}^{5} g_{1}^{3} g_{2} - 42 f_{1}^{4} f_{2}^{6} g_{1}^{3} g_{2} + 2 f_{1}^{3} f_{2}^{7} g_{1}^{3} g_{2} + f_{1}^{8} f_{2}^{2} g_{1}^{2} g_{2}^{2} + 22 f_{1}^{7} f_{2}^{3} g_{1}^{2} g_{2}^{2} + 120 f_{1}^{6} f_{2}^{4} g_{1}^{2} g_{2}^{2} + 120 f_{1}^{4} f_{2}^{6} g_{1}^{2} g_{2}^{2} \\
& - 22 f_{1}^{3} f_{2}^{7} g_{1}^{2} g_{2}^{2} + f_{1}^{2} f_{2}^{8} g_{1}^{2} g_{2}^{2} - 2 f_{1}^{7} f_{2}^{3} g_{1} g_{2}^{3} - 42 f_{1}^{6} f_{2}^{4} g_{1} g_{2}^{3} - 194 f_{1}^{5} f_{2}^{5} g_{1} g_{2}^{3} + 282 f_{1}^{4} f_{2}^{6} g_{1} g_{2}^{3} - 46 f_{1}^{3} f_{2}^{7} g_{1} g_{2}^{3} \\
& + 2 f_{1}^{2} f_{2}^{8} g_{1} g_{2}^{3} + f_{1}^{6} f_{2}^{4} g_{2}^{4} + 22 f_{1}^{5} f_{2}^{5} g_{2}^{4} + 119 f_{1}^{4} f_{2}^{6} g_{2}^{4} - 22 f_{1}^{3} f_{2}^{7} g_{2}^{4} + f_{1}^{2} f_{2}^{8} g_{2}^{4} - 2 f_{1}^{7} f_{2} g_{1}^{5} - 110 f_{1}^{6} f_{2}^{2} g_{1}^{5} \\
& - 166 f_{1}^{5} f_{2}^{3} g_{1}^{5} - 12 f_{1}^{4} f_{2}^{4} g_{1}^{5} - 4 f_{1}^{7} f_{2} g_{1}^{4} g_{2} - 242 f_{1}^{6} f_{2}^{2} g_{1}^{4} g_{2} - 450 f_{1}^{5} f_{2}^{3} g_{1}^{4} g_{2} - 438 f_{1}^{4} f_{2}^{4} g_{1}^{4} g_{2} - 24 f_{1}^{3} f_{2}^{5} g_{1}^{4} g_{2} \\
& - 2 f_{1}^{7} f_{2} g_{1}^{3} g_{2}^{2} - 142 f_{1}^{6} f_{2}^{2} g_{1}^{3} g_{2}^{2} + 62 f_{1}^{5} f_{2}^{3} g_{1}^{3} g_{2}^{2} + 110 f_{1}^{4} f_{2}^{4} g_{1}^{3} g_{2}^{2} - 370 f_{1}^{3} f_{2}^{5} g_{1}^{3} g_{2}^{2} - 10 f_{1}^{2} f_{2}^{6} g_{1}^{3} g_{2}^{2} - 10 f_{1}^{6} f_{2}^{2} g_{1}^{2} g_{2}^{3} \\
& + 370 f_{1}^{5} f_{2}^{3} g_{1}^{2} g_{2}^{3} + 110 f_{1}^{4} f_{2}^{4} g_{1}^{2} g_{2}^{3} - 62 f_{1}^{3} f_{2}^{5} g_{1}^{2} g_{2}^{3} - 142 f_{1}^{2} f_{2}^{6} g_{1}^{2} g_{2}^{3} + 2 f_{1} f_{2}^{7} g_{1}^{2} g_{2}^{3} + 24 f_{1}^{5} f_{2}^{3} g_{1} g_{2}^{4} - 438 f_{1}^{4} f_{2}^{4} g_{1} g_{2}^{4} \\
& + 450 f_{1}^{3} f_{2}^{5} g_{1} g_{2}^{4} - 242 f_{1}^{2} f_{2}^{6} g_{1} g_{2}^{4} + 4 f_{1} f_{2}^{7} g_{1} g_{2}^{4} - 12 f_{1}^{4} f_{2}^{4} g_{2}^{5} + 166 f_{1}^{3} f_{2}^{5} g_{2}^{5} - 110 f_{1}^{2} f_{2}^{6} g_{2}^{5} + 2 f_{1} f_{2}^{7} g_{2}^{5} + f_{1}^{6} g_{1}^{6} \\
& + 152 f_{1}^{5} f_{2} g_{1}^{6} + 48 f_{1}^{4} f_{2}^{2} g_{1}^{6} + 2 f_{1}^{6} g_{1}^{5} g_{2} + 340 f_{1}^{5} f_{2} g_{1}^{5} g_{2} + 300 f_{1}^{4} f_{2}^{2} g_{1}^{5} g_{2} + 96 f_{1}^{3} f_{2}^{3} g_{1}^{5} g_{2} + f_{1}^{6} g_{1}^{4} g_{2}^{2} + 212 f_{1}^{5} f_{2} g_{1}^{4} g_{2}^{2} \\
& - 312 f_{1}^{4} f_{2}^{2} g_{1}^{4} g_{2}^{2} - 394 f_{1}^{3} f_{2}^{3} g_{1}^{4} g_{2}^{2} + 24 f_{1}^{2} f_{2}^{4} g_{1}^{4} g_{2}^{2} + 24 f_{1}^{5} f_{2} g_{1}^{3} g_{2}^{3} - 540 f_{1}^{4} f_{2}^{2} g_{1}^{3} g_{2}^{3} - 540 f_{1}^{2} f_{2}^{4} g_{1}^{3} g_{2}^{3} - 24 f_{1} f_{2}^{5} g_{1}^{3} g_{2}^{3}\\
& + 24 f_{1}^{4} f_{2}^{2} g_{1}^{2} g_{2}^{4} + 394 f_{1}^{3} f_{2}^{3} g_{1}^{2} g_{2}^{4} - 312 f_{1}^{2} f_{2}^{4} g_{1}^{2} g_{2}^{4} - 212 f_{1} f_{2}^{5} g_{1}^{2} g_{2}^{4} + f_{2}^{6} g_{1}^{2} g_{2}^{4} - 96 f_{1}^{3} f_{2}^{3} g_{1} g_{2}^{5} + 300 f_{1}^{2} f_{2}^{4} g_{1} g_{2}^{5} \\
& - 340 f_{1} f_{2}^{5} g_{1} g_{2}^{5} + 2 f_{2}^{6} g_{1} g_{2}^{5} + 48 f_{1}^{2} f_{2}^{4} g_{2}^{6} - 152 f_{1} f_{2}^{5} g_{2}^{6} + f_{2}^{6} g_{2}^{6} - 64 f_{1}^{4} g_{1}^{7} - 144 f_{1}^{4} g_{1}^{6} g_{2} - 128 f_{1}^{3} f_{2} g_{1}^{6} g_{2} \\
& - 92 f_{1}^{4} g_{1}^{5} g_{2}^{2} + 264 f_{1}^{3} f_{2} g_{1}^{5} g_{2}^{2} + 32 f_{1}^{2} f_{2}^{2} g_{1}^{5} g_{2}^{2} - 12 f_{1}^{4} g_{1}^{4} g_{2}^{3} + 296 f_{1}^{3} f_{2} g_{1}^{4} g_{2}^{3} + 4 f_{1}^{2} f_{2}^{2} g_{1}^{4} g_{2}^{3} + 96 f_{1} f_{2}^{3} g_{1}^{4} g_{2}^{3} \\
& - 96 f_{1}^{3} f_{2} g_{1}^{3} g_{2}^{4} + 4 f_{1}^{2} f_{2}^{2} g_{1}^{3} g_{2}^{4} - 296 f_{1} f_{2}^{3} g_{1}^{3} g_{2}^{4} - 12 f_{2}^{4} g_{1}^{3} g_{2}^{4} + 32 f_{1}^{2} f_{2}^{2} g_{1}^{2} g_{2}^{5} - 264 f_{1} f_{2}^{3} g_{1}^{2} g_{2}^{5} - 92 f_{2}^{4} g_{1}^{2} g_{2}^{5} \\
& + 128 f_{1} f_{2}^{3} g_{1} g_{2}^{6} - 144 f_{2}^{4} g_{1} g_{2}^{6} - 64 f_{2}^{4} g_{2}^{7} - 128 f_{1}^{2} g_{1}^{6} g_{2}^{2} - 80 f_{1}^{2} g_{1}^{5} g_{2}^{3} - 128 f_{1} f_{2} g_{1}^{5} g_{2}^{3} + 48 f_{1}^{2} g_{1}^{4} g_{2}^{4} + 48 f_{2}^{2} g_{1}^{4} g_{2}^{4} \\
& + 128 f_{1} f_{2} g_{1}^{3} g_{2}^{5} - 80 f_{2}^{2} g_{1}^{3} g_{2}^{5} - 128 f_{2}^{2} g_{1}^{2} g_{2}^{6} - 64 g_{1}^{5} g_{2}^{4} - 64 g_{1}^{4} g_{2}^{5}. \end{align*}
    \caption{Expression for $J^2$ in terms of the basic forms $f_1, f_2, g_1, g_2$}
    \label{fig:my_label}
\end{figure}

\bibliographystyle{plainnat}
\bibliofont

redpajama_set_name: RedPajamaArXiv


Navarro who proposed my blog for this award.
Answered yes or no : Are you aware of the statistics?
something for the woman in your blog?
situation of pregnant women in your country?
lingerie fashion show 'Victoria's Secret'?
feel offended just by calling her 'fat'?
1. At what age did you make your first craft?
2. Have you relative education?
5. Excluding crafts what is your hobby?
6. Your relationship with dance?
7. What kind of literary books do you prefer?
8. Do you like to watch TV?


Beautiful banner by Benni and great theme by Mitch.
A glimpse of the rescue boat.
There one second, gone the next!!
A glimpse of sunlight behind the clouds.
Hi Anders!! Good choices for the theme. I like the glimpse of the modern lifeboat compared to the old-fashioned sailing ship. Yes, fireworks are fleeting glimpses of beauty. I love the patterns of the clouds in the third shot.
Hi Anders! All the three are different... all the three are perfect for the theme!


text:
Q: Can I tell Linux not to swap out a particular processes' memory? Is there a way to tell Linux that it shouldn't swap out a particular processes' memory to disk?
Its a Java app, so ideally I'm hoping for a way to do this from the command line.
I'm aware that you can set the global swappiness to 0, but is this wise?

A: There exist a class of applications in which you never want them to swap. One such class is a database. Databases will use memory as caches and buffers for their disk areas, and it makes absolutely no sense that these are ever put to swap. The particular memory may hold some relevant data that is not needed for a week until one day when a client asks for it. Without the caching/swapping, the database would simply find the relevant record on disk, which would be quite fast; but with swapping, your service might suddenly be taking a long time to respond.
mysqld includes code to use the OS / system call memlock. On Linux, since at least 2.6.9, this system call will work for non-root processes that have the CAP_IPC_LOCK capability[1]. When using memlock(), the process must still work within the bounds of the LimitMEMLOCK limit. [2]. One of the (few) good things about systemd is that you can grant the mysqld process these capabilities, without requiring a special program. If can also set the rlimits as you'd expect with ulimit. Here is an override file for mysqld that does the requisite steps, including a few others that you might need for a process such as a database:
[Service]
# Prevent mysql from swapping
CapabilityBoundingSet=CAP_IPC_LOCK

# Let mysqld lock all memory to core (don't swap)
LimitMEMLOCK=-1

# do not kills this process if low on memory
OOMScoreAdjust=-900

# Use higher io scheduling
IOSchedulingClass=realtime

Type=simple
ExecStart=
ExecStart=/usr/sbin/mysqld --memlock $MYSQLD_OPTS

Note The standard community mysql currently ships with Type=forking  and adds --daemonize in the option to the service on the ExecStart line. This is inherently less stable than the above method.
UPDATE I am not 100% happy with this solution. After several days of runtime, I noticed the process still had enormous amounts of swap! Examining /proc/XXXX/smaps, I note the following:

*

*The largest contributor of swap is from a stack segment! 437 MB and fluctuating. This presents obvious performance issues. It also indicates stack-based memory leak.

*There are zero Locked pages. This indicates the memlock option in MySQL (or Linux) is broken. In this case, it wouldn't matter much because MySQL can't memlock stack.

A: You can do this via the mlockall(2) system call under Linux; this will work for the whole process, but do read about the argument you need to pass.
Do you really need to pull the whole thing in-core?  If it's a java app, you would presumably lock the whole JVM in-core.  I don't know of a command-line method for doing this, but you could write a trivial program to call fork, call mlockall, then exec.
You might also look to see if one of the access pattern notifications in madvise(2) meets your needs.  Advising the VM subsystem about a better paging strategy might work out better if it's applicable for you.
Note that a long time ago now under SunOS, there was a mechanism similar to madvise called vadvise(2).

A: You can do that by the mlock family of syscalls. I'm not sure, however, if you can do it for a different process.

A: As super user you can 'nice' it to the highest priority level -20 and hope that's enough to keep it from being swapped out. It usually is. Positive numbers lower scheduling priority. Normal users cannot nice upwards (negative nos.)

A: If you wish to change the swappiness for a process add it to a cgroup and set the value for that cgroup:
https://unix.stackexchange.com/questions/10214/per-process-swapiness-for-linux#10227

A: Except in extremely unusual circumstances, asking this question means that You're Doing It Wrong(tm).
Seriously, if Linux wants to swap and you're trying to keep your process in memory then you're putting an unreasonable demand on the OS. If your app is that important then 1) buy more memory, 2) remove other apps/daemons from the machine, or dedicate a machine to your app, and/or 3) invest in a really fast disk subsystem. These steps are reasonable for an important app. If you can't justify them, then you probably can't justify wiring memory and starving other processes either.

A: Why do you want to do this?
If you are trying to increase performance of this app then you are probably on the wrong track. The OS will swap out a process to increase memory for disk cache - even if there is free RAM, the kernel knows best (actauly the samrt guys that wrote the scheduler know best).
If you have a process that needs responsiveness (it's swapped out while not used and you need it to restart quickly) then nice it to high priority, mlock, or using a real  time kernel might help.

redpajama_set_name: RedPajamaStackExchange


In advance of the upcoming twentieth anniversary of the original release (May 7, 1992) of "Baby Got Back," his chart-topping multi-platinum Grammy-winning hip-hop celebration of female pulchritude, Seattle-based rap icon (and Sony Music Entertainment/Legacy Recordings artist) Sir Mix-a-Lot is bustin' out his Baby Got Back app, the ultimate 21st century booty-based app, exclusively for the iPhone.
Sir Mix-a-Lot's Baby Got Back app comes fully-packed with a buttload of hands-on features including the Mix Makeover photo lab, the Ba Dunka Dunk club game, Sir Mix-a-Lot's Booty Calls, a social media Text Mix and more. As a deluxe visual bonus, the Baby Got Back app includes the old school but still-hot-and-hilarious "Baby Got Back" music video (briefly banned by MTV in 1992).
Baby Got Back's Mix Makeover photo feature allows you to take a new or existing photo and manipulate any aspect that appeals. With the twist of your fingers, you can blow-up and stretch any visual assets–fore and aft, tops or bottoms–to suit individual taste before sharing the results with friends.
The Ba Dunka Dunk game is a fast-paced romp through a virtual clubland where back and booty rule. The aim is to fill hot pants in motion as you tilt your device from side-to-side, maneuvering the booty girls around obstacles and into the right fit. The better you get, the faster the action.
On Sir Mix-a-Lot's Booty Calls, you can hear the master get down to business and draw the fine distinctions between Da Onion, Donkey, Switch & Drop, the Hip Gripper, the Palm, the Crash Helmet, or Thong blesser.
Fans can be part of Sir Mix-a-Lot's posse through the Baby Got Back app's Text Mix feature.
Originally released in 1992, Sir Mix-a-Lot's single "Baby Got Back" (from his Mack Daddy album on Def American) launched a million parties with its unapologetic and unambiguous rallying opening cry, "I like big butts and I cannot lie….," a statement so strong it cannot be denied. The controversial single spent five weeks at Number One on the Hot 100 in the summer '92, sold double platinum in the United States, picked up 1993's Grammy for Best Rap Solo Performance and added the phrase "Baby Got Back" to the cultural lexicon.
The Sir Mix-a-Lot Baby Got Back iPhone app is the next step in the evolving legacy of a timeless track that continues to put bottoms on top.


As the Democratic Convention wound down, Vice President George Bush accused Michael Dukakis of being "a card-carrying member of the American Civil Liberties Union."
I do have a prejudice touching this disturbing echo of the injustices of the McCarthy era. My prejudice is that the United States is the greatest political invention of modern times. Recognizing the need to protect the individual from the crushing power of the state, the founders gave us a Bill of Rights which made the greatness of our democracy possible.
In using a variation of Sen. Joe McCarthy's "three-C phrase" (card-carrying communist), Bush employed another evil trick used by the senator. Guilt by association is a sneak's way of injustice.
The possibility that this unfortunate lapse to one of the more unproud times of our republic was created at the top level of Bush's staff was enhanced when Patrick Buchanan repeated the phrase on television. Buchanan is not the most temperate speech writer to have worked in the White House.
As vice president of ACLU of Southern California, I could carry a membership card if I felt a need to do so. Therefore, the brain trust that wrote this phrase for Bush (I do not believe he wrote it himself) attacked me. Of what am I and others who love freedom from government oppression accused?
Bush's slogan makers were true poets. They dredged up memories of scoundrels like McCarthy without actually accusing me of the sin of "C". I don't feel smeared. I don't feel slurred. There is something effete about their work. I stand accused of belonging to an organization to which Bush does not belong. I certainly would resist any attempt to discover if Bush is a closeted member of ACLU.
Do you suppose that Bush's brain trust gasped when ACLU sued for dismissal of the charges against Oliver North on constitutional grounds? They should not have. They should know that ACLU believes the Constitution protects everyone, even them.
Our Constitution protects Bush--even if he does talk funny.


With a stay at La Quinta by Wyndham O'Fallon, IL - St. Louis in O'Fallon, you'll be within a 5-minute drive of O'Fallon Family Sports Park and St. Clair Bowl. This hotel is 3.5 mi (5.7 km) from St. Claire Square Mall and 4 mi (6.4 km) from Far Oaks Golf Course.
Make yourself at home in one of the 63 air-conditioned rooms featuring refrigerators and flat-screen televisions. Your pillowtop bed comes with premium bedding. Complimentary wired and wireless Internet access keeps you connected, and cable programming provides entertainment. Private bathrooms with shower/tub combinations feature complimentary toiletries and hair dryers.
Special requests are subject to availability upon check-in and may incur additional charges. Special requests cannot be guaranteed. Please note that cultural norms and guest policies may differ by country and by property. The policies listed are provided by the property. Valid credit card required upon check-in.


text:
Q: How to disable UIBarButtonItem? I have a UIBarButtonItem that just doesn't want to get disabled. Short version: when I call
[myBarButtonItem setEnabled:NO];

Nothing happens.
myBarButtonItem is an IBOutlet in myVIewController. myViewController has been added as an object to MainWindow in Interface Builder. The myBarButtonItem outlet has been connected to the BarButtonItem, and has the corresponding @syntesize and property lines set.
@property (nonatomic, retain) IBOutlet UIBarButtonItem *myBarButtonItem;

In myViewController.m,
@synthesize myBarButtonItem;

Anyone have an idea why the above setEnabled method has no affect? Thanks!
UPDATE: Fixed it! Don't know why, but apparently the outlet wasn't being set. I used my App Delegate as the parent object for the UIBarButtonItem, and all worked out.

A: You can disable the left navigation button from inside an UIViewController like this, without using any IBOutlet:
self.navigationItem.leftBarButtonItem.enabled = NO;

To disable the right navigation button:
self.navigationItem.rightBarButtonItem.enabled = NO;

Swift3
self.navigationItem.rightBarButtonItem?.isEnabled = false

A: I used a different solution (Swift 4.2) for my rightBarButtonItems.
I had 3 buttons so used a for loop, then made an extension of UINavigationItem so I could use it throughout my app.
extension UINavigationItem {
func setRightBarButtonItems(isEnabled:Bool){
    for button in self.rightBarButtonItems ?? [UIBarButtonItem()] {
        button.isEnabled = isEnabled
    }
}

Then i can call it from my TableViewController
navigationItem.setRightBarButtonItems(isEnabled: false)

A: In my case (Swift) I had 2 barButtonItems added as an array - so to disable them this did the trick
    navigationItem.rightBarButtonItems?.first?.enabled = false
    navigationItem.rightBarButtonItems?.last?.enabled = false

A: If your toolbar has an IBOutlet (and you've checked to make sure it's non-nil), try:
[ [ [ myToolBar items ] objectAtIndex: myBarButtonItemIndex ] setEnabled:(NO) ];


Multan (Friday, October 10th, 2014): The board of intermediate & secondary education Multan board is here to declare the Intermediate part-1 (11th Class) result 2014 on Friday 10/10/2014.
The bise Multan result of FA/FSc Part1 result for Science and arts group will be announced on 10.10.2014 by Multan board. The bise Multan inter part1 result 2014 will be Uploaded on October 10, 2014 at 10:10 AM.
The inter part 1 result of Bise Multan Board (Fa / Fsc inter result 2014) will be uploaded on this pages.
The Multan Board Inter Part 1-11th Class Position holders will be uploaded on official website on Bise Multan. The Position Holders ceremony will be held by Boards Offices in their boards.
The FA FSc part 1 result will be also available on official website on Bise Multan.


text:
International Journal of Biological Innovations
Publisher: Global Environmental & Social Association (GESA)
Country of publisher: india
Date added to EuroPub: 2020/May/15
LCC Subject Category: Biological Sciences
Publisher's keywords: Biological Sciences, Zoology, Botany, Agriculture, Biotechnology, Environment
Waiver policy for charges? Yes
Type of License:
Does the author retain unrestricted copyright? True
Content digitally archived in: Other
Deposit policy registered in:
Select Filter Year: 2020 , Volume: 2 , Number: 2 Year: 2020 , Volume: 2 , Number: 1 Year: 2019 , Volume: 1 , Number: 2 Year: 2019 , Volume: 1 , Number: 1
COVID-19 : TOWARDS CONFRONTING AN UNPRECEDENTED PANDEMIC
Authors: Tamanna Kumari and Vineeta Shukla
International Journal of Biological Innovations 2020/May/15
Latest 73rd report of COVID-19 from national authorities to WHO by April 2, 2020, there are 896450 confirmed cases with 45526 deaths globally. 0 to 14 days is the average range of incubation period. Recent study from China Center for disease control (CDC) showed that most of the patients were asymptomatic in its early days of infection that leads to widespread of virus. Nosocomial transmission is another serious problem the world is facing with this public health crisis. Corona viruses are known to cause respiratory and enteric disease in human and animals. These are round or oval and pleomorphic in shape. Limited information is present till now about COVID-19. It suggests that its infection ranges from previous corona virus encounters. Here in this review we summarize all information present till date and also a brief comparison to SARS and MERS. This is to identify the gaps in knowledge to share resources to recover from COVID-19. It also includes pharmaceutical drugs that showed a negative impact on SARS-CoV- 2 in in-vitro studies that can be used for its treatment till a suitable vaccine candidate is available. The most important task at this hour is to find a vaccine for the infection. Moreover, the research needs to be conducted for finding measures to face this kind of challenges in future.
Keywords: Clinical manifestation, Epidemiology of COVID-19, Outbreak, Prevention, Viral mystery.
EFFECT OF ARSENIC ON SERUM BIOCHEMICAL PARAMETERS OF A FRESH WATER CAT FISH, MYSTUS VITTATUS
Authors: Sadguru Prakash and Ashok Kumar Verma
The present investigation has been designed to study the effect of sublethal concentrations (10% and 30%) of heavy metal, arsenic on the serum metabolites, serum enzyme activity and serum electrolytes of Mystus vittatus after exposure to 30 days. The present study shows that serum metabolites such as glucose, protein and bilirubin were significantly decreased while free amino acid, triglyceride and cholesterol were significantly increased; serum enzymes such as acid phosphatase (ACP), transminases (SGPT & SGOT) were increased significantly while alkaline phosphatase (ALP), was decreased significantly; serum electrolytes such as sodium, potassium and calcium were decreased significantly but chloride was increased significantly. Thus, this paper gives an overview of the manipulation of fish, Mystus vittatus as a biomarker of heavy metals through alternation in biochemical parameters.
Keywords: Arsenic, Electrolytes, Enzyme activities, Metabolites, Mystus vittatus.
DECLINE OF HOUSE SPARROW AND COMMON MYNA POPULATION IN DODA REGION OF JAMMU AND KASHMIR, INDIA
Authors: Wahied Khawar Balwan and Neelam Saba
The House Sparrow (Passer domesticus) and Common Myna (Acridotheres tristis),once very common birds, have declined markedly in most parts of the India including Doda district of Jammu and Kashmir. Once these birds were distributed widely in Doda district but over the past few years, they became not so common in this region. A study has been conducted during April 2016 to April 2020 to establish the database for their current populationand to assess the possible causes of their decline in Doda district. The house sparrow is a symbiotic bird species highly adaptable with human habitation.House construction due to modern trend has resulted in reduced safe nesting for sparrows and mynas. Green spaces in our cities give way to more concrete construction due to which the house sparrow and myna loses its foraging ground. There is a dire need of ecological balancing to save the Sparrows and Mynas from getting extinct.
Keywords: Acridotheres tristis, Conservation, Doda, Passer domesticus.
MACROPHYTES AS BIOINDICATOR IN BICHHIYA RIVER, REWA (M.P.), INDIA
Authors: Srishti Singh and Suman Singh
The present study was aimed to analyze the macrophytes as bioindicators in Bichhiya River at Rewa. The study was conducted over a period of one year from January 2019 to December 2019 at 3 different sampling stations selected for the purpose in Rewa, a district of Madhya Pradesh, India. The physico-chemical parameters of water such as temperature, pH, DO, BOD, COD, hardness which are most useful for the prediction of distribution of macrophytes were analysed. A sum of 30 species of macrophytes was identified. Presence of macrophytes (1) reflects the nutrients enrichment and organic loading and (2) indicates the water pollution. Abundance and high density of Ceratophyllum demersum, Nitella hyalina, Chara vulgaris, Potamogeton pectinata indicated the enrichment of nutrients and high organic loading.
Keywords: Bichhiya River, Bioindicator, Macrophytes, Rewa, Water Quality_
CALCIUM IN PLANT BIOLOGY: NUTRIENT AND SECOND MESSENGER
Authors: Rachana Singh
Calcium (Ca2+ ) is an essential element required for growth and development of plants both under stressed and non-stressed situations. It not only maintains the integrity of cell wall and membrane, but also serves as a second messenger in many developmental and physiological processes thereby inducing Ca2+ influx into cytosol, which decodes into downstream responses like defense against various environmental cues. Therefore, maintenance of intracellular Ca2+ homeostasis is essential for Ca2+ signalling. In this review, the current knowledge about the Ca2+ uptake, transport and signal transduction in different physiological aspects with respect to plant nutrient status will be discussed.
Keywords: Calcium, Kinases, Nutrient signalling, Plant immunity, Second messenger.
CLINICAL MANIFESTATIONS AND PROTECTIVE MEASURES OF ENVIRONMENTAL NOISE: AN OVERVIEW
Authors: Raaz K. Maheshwari, Ranjeet Poonia, Mahendra Singh Rathore, Ashok K. Kakodia, Anil Kumar and Sulochna Sharma
Noise pollution (or environmental noise) refers to unwanted or unpleasant sound that disrupts the activity or balance of human and animal life. It reduces the concentration and negatively affects the mental activity. The noise is generated by the human through various ways and activities. Noise must be controlled and prevented by using various effective techniques at the source itself is today's need. This review basically discuss the various sources of noise pollution, measurement of noise, dB scale, equipments used in the measurement of noise levels, adverse effects of noise pollution on health, control of indoor noise, control technologies available for noise pollution and Indian penal codes to prevent noise pollution are the main points of focus of attention.
Keywords: Behavioral problems, Cardiovascular, Cognitive performance, dB, Psychological stress_
CLIMATE CHANGE AND PRACTICES OF FARMERS' TO MAINTAIN RICE YIELD: A CASE STUDY
Authors: Amar Chandra Mandal and Om Prakash Singh
A survey was conducted during December 2019 to March 2020 in the Siraha district of Nepal to assess farmers' perception on climate change and identifications of local practices to maintain the yield of rice production. Total 60 samples were purposively selected from the study site. During interaction and interview, the opinion of 75- 80% formers was that temperature increases, rainfall duration and its frequency decreases due to the global warming. About 33.33% farmers experience was an increase in flooding hazard due to increase in rainfall intensity during the rainy season in Siraha and its vicinity. The majority of respondents perceived increased in weed and pest (65%) and new weed (30%) and new pest (26.7%) infestation due to climate change. About 18% respondents had a clear knowledge of climate change. The major source of information was selfexperiences (80%) and organization (20%). The major climate change adaptation practices adopted by farmers were the use of drought-resistant varieties (11.67%), flood-resistant varieties (13.33%) and early maturing crops (15%). Crop insurance is one of the adaptation practices to climate change. The study showed that 63.33 % of the respondents know about crop insurance policy but none of the respondents have done crop insurance on different crops. The increase in disease and pest infestation is major problems of farmers. The focus group discussion and key informant study showed that the farmers were positive to adopt climate change adaptation strategies. So, Government and policymakers should focus on climate-resilient adaptation strategies formulation for rice cultivation through intensive research and extension package. Adoption of different resistant varieties and technological adoption like zero tillage, application of irrigation, and training related to adoption techniques should be done.
Keywords: Climate change, Global warming, Perception, Rainfall, Rice production_
HOLISTIC SURVEY ON PREDATORY LADYBIRD BEETLE DIVERSITY AT SELECTED REGIONS OF NASHIK DISTRICT (MAHARASHTRA), INDIA
Authors: Shaikh Yasmeen* and Punam Dugaje
A survey was conducted during January 2016 to December 2017 in four sites of Nashik to study the diversity of the predatory beetles. During the present study, a total of 14 species belonging to 11 genera and 4 subfamilies were recorded from the area studied. Subfamily Chilorinae is represented by 2 species belonging to 2 genera, Subfamily Coccinellinae by 8 species belonging 6 genera, Subfamily Scymninae by 2 species belonging to 2 genera and Subfamily Sticholotidinae by 2 species belonging to the same single genus from the different sites of the study area. The Subfamily Coccinellinae was the most variant and abundant among all the four subfamilies.
Keywords: Biodiversity, Coccinellids, Fauna, Ladybird beetles, Nashik_
REVERSAL OF HYPERMETHYLATION AND REACTIVATION OF TUMOR SUPPRESSOR GENES DUE TO NATURAL COMPOUNDS IN BREAST CANCER CELLS
Authors: Debasray Saha, Neeraj Vaishnav, Zubiya Ahsan, Nisha Rani, Runjhun Mathur and Abhimanyu Kumar Jha
Breast oncogenesis is a multistage process that involves epigenetic and genetic changes. Epigenetics is outlined as reversible changes in gene expression, with no alteration in gene sequence. DNA methylation, histone modification, and nucleosome transformation are the foremost epigenetic changes that may get dysregulated in breast cancer. Epigenetic silencing of tumor suppressor genes (TSGs) is reversed by varied molecules as well as natural compounds like polyphenols which will act as a hypermethylation agent. Nowadays, much of the research is going in the direction of natural and dietary compounds and attempting to search out novel and extra effective medical aid for the breast cancer patients. In this literature, few vital natural chemical compounds effective against the breast oncogenesis with their mode of actions are discussed. Such chemicals act as an analytical and prognostic tool in breast cancer due to their role in epigenetic regulation.
Keywords: DNA methylation, Epigenetics, Gene expression, Oncogenesis, Tumor suppressor gene_
A SURVEY OF FISH FAUNA OF RAPTI RIVER, BALRAMPUR (U.P.), INDIA
Authors: Sudhakar Prakash , Ashok Kumar , Shri Prakash and B.K. Mishra
An initial survey was under taken to study the occurrence and diversity of fishes in Rapti River flowing through Balrampur district of Uttar Pradesh, India. The present survey was conducted from January, 2018 to December, 2018 to find out the fish fauna of Rapti River at Balrampur district. A total of 27 species of fishes belonging to 19 genera, 14 families and 7 orders were identified as a preliminary survey and observation. This was the first systematic survey on the fish diversity of this River. Order Siluriformes was found most dominant represented by 10 species, followed by Cypriniformes with 7 species; Perciformes and Ophiocephaliformes with 3 species each; Osteoglossiformes with 2 species while Clupeiformes and Beloniformes with only one species each.
Keywords: Cypriniformes, Fish Diversity, Rapti River, Siluriformes_
Comparative Analysis of Sarus Crane Population from 2012-2019 in and around Alwara Lake of District Kaushambi (U.P.), India
Authors: Shri Prakash and Ashok Kumar Verma
The present study is designed to analyze the population of Indian Sarus Crane (Grus antigone antigone) in and around the Alwara Lake of district Kaushambi (Uttar Pradesh) India in 8 consecutive years from 2012 to 2019. The sarus crane is the only resident and non-migratory breeding crane of Indian subcontinent. This bird is now globally threatened due to the shrinking in the extent and quality of their wetland habitats, reduction in suitable mating sites and increased anthropogenic activities. In the present study, authors attempted to count the number of sarus crane in 8 consecutive years from 2012 to 2019 in the same study area. This systematic analysis reflects an increase in the number of sarus crane at sustainable level in the area studied.
Keywords: Alwara Lake, Conservation, Sarus crane, Threatened, Wetland_
Status of Indian major carps spawn in the Halda River along with marketing and economic condition of the Fishers and related collectors
Authors: B.K. Chakraborty, M.H. Shahroz, A.B. Bhuiyan, S. Bhattacharjee and S. Chattoraj
The spawn of Indian major carps makes the Halda River an irreplaceable heritage of Bangladesh. The study was conducted to observe present status of Indian major carp breeding and collection management procedures of carp spawn and fry from the Halda River along with marketing process and economic conditions of the fishers and spawn collector. Data were collected through direct interview. In marketing system of carp eggs, spawn and fry in the Halda River, a number of intermediaries were involved actively in the marketing system. Four different types of marketing systems were identified in Halda spawn and fry distribution fry seller to final consumer. Fertilized eggs and spawn were collected and hatched by the local fisher's and collectors using their indigenous method. Those egg collectors sold to the hatchery owners per kg spawn at the rate of 50,000-80,000 BdTk. Again hatchery owners sold each and every fry at the rate of 5.0-6.0 BDTk. to the local fish farmers. Yearly survey information on Halda River's egg, spawn and fry collection showed an ups and downs production rate during last 07 years. The production status in the year 2011, 2012, 2013, 2014, 2015, 2016 and 2017 was 230, 1569, 526, 508, 107, 320 and 338kg respectively and these types of ups and downs indicated poor number of broods, poor breeding ground and poor ecosystem of the Halda River. Different types of transports were used to carry fertilized eggs and spawn of Halda River. Investigation was also done to find out the economic condition, average income during breeding season and off season, educational background and family status of the local people of Halda region involving in fry collecting and marketing system. The study recommends that ecosystem health and breeding ground of Halda River should be protected for ensuring availability of pure line fertilized eggs and spawn of Indian major carp.
Keywords: Economic resources, Fertilized egg, Halda River, Marketing, Production, Spawn_
Diversity of Parthenium hysterophorus and associated weeds in the Chitrakoot District
Authors: Preeti Tripathi and Ramesh Chandra
Parthenium hysterophorus L. (Carrot grass) is an annual herb of neotropical origin that now has a serious problem and pantropical distribution. It was first reported in India in 1950 at Pune (Maharashtra). This weed is very aggressive and commonly known as Congress grass and carrot grass in India. It has achieved major weed status in India within a relatively short period of time. P. hysterophorus is grown mostly in cultivated fields, fallow lands, pasture and along the roadsides. To analyse the distribution of this weed in Chitrakoot district an exhaustive survey was performed in the holly place of Uttar Pradesh like Rajapur, Pahadi, Karwi and M.G.C.G.V. campus. During survey, the distribution of P. hysterophorus was measured in the agricultural lands, road side, river side and fallow lands. Moreover, the study also investigated the harmful effect of Parthenium upon native weeds and flora in the Chitrakoot district. Quadrates method (1mx1m) was used to collect the data of distribution and population of this weed. In this investigation, total 14 weed species were recorded belonging to 8 different families and 14 genera. The data were recorded by Absolute density (m2), relative density (%), absolute frequency (%), relative frequency (%) and importance value (%) of Parthenium and other associated weeds. The finding reveals that Parthenium weed is the most dominant species in comparison to other associated weeds. In conclusion, the Parthenium weed become a serious problem and replaces the entire native flora in the non-crop area. Due to no proper management and high growth rate, nowadays it becomes as super weed in the Chitrakoot district. So, the management of Parthenium weed requires the call attention from the Government Policy makers and proper quarantine inspection to conserve the native flora and fields crops to get maximum crop yield.
Keywords: Absolute density, Absolute frequency, Relative density, Relative frequency, Value, Zygogramma_
Incredible Benefits of Exotic Kiwano (Horned Melon) for Wellness, Vigour and Vitality
Authors: Bina Rani, Upma Singh, Lakha Ram, Ravi Sharma, Harsukh Chharang, Anju Sharma and Raaz K Maheshwari
The kiwano belongs to the Cucumber family. The alien looking fruit has similarities with Pomegranate and Passion fruit in its texture and is a traditional food plant in the African continent. Its increasing popularity in the health arena is due to the abundance of health benefits it possesses. It improves cognitive function, used as a recovery aid for heart stroke; kiwano melon slows down the ageing process and even neutralizes the free radicals in the body. The high fiber content in kiwano makes it an ideal digestive aid. Due to the presence of essential nutrients, minerals and organic compounds in the fruit, it got recognition by WHO, stating kiwano to be an essential fruit in fighting against illness and malnutrition. The health benefits of the kiwano are in the nutrients it contains including vitamin C, Fe and K. It also has smaller amounts of P, Mg, Zn, Ca, Cu, and Na. The seeds contain linoleic and oleic acid. Linoleic acid is an omega fatty acid which is required for human health while oleic acid is thought to help in lowering the blood pressure. A couple of anti-oxidants recognized in kiwano seeds are α-tocopherol as well as β-tocopherol. The yellowish-green colored pigments are located at the seeds. Its pulp contains the carotenoid, beta carotene. The beta carotene strengthens the body's defense mechanisms and sustains eye and skin health. It may also help to prevent cancer simply by suppressing the growth of free-radicals. This review article is aimed to discuss the diseases or ailments that are treated with the plant Cucumis metuliferus.
Keywords: Fatty acids, Free radicals, Illness, Malnutrition, Minerals, Tocopherol_
Impact of Climate Change on Biodiversity: An Overview
Authors: Sadguru Prakash1 and Seema Srivastava
Biodiversity is the 'Full variety of Life on Earth'. It includes diversity within species, between species and of ecosystem. Biodiversity plays an important role in climate regulation. Biodiversity conservation will lead to strengthening of ecosystem resilience and will improve the ability of ecosystem to provide important services during increasing climate pressures. But due to anthropogenic activities the global climate has changed since last few decades.This climate change adversely affected the biological resources of the country. This review basically discuss the importance of biodiversity, the consequences faced by the plants, animals, humans and ecosystem owing to the climate change and also control measures or strategies should be taken for the conservation of biodiversity which can protect the earth from the consequence of climate change.
Keywords: Biodiversity, Climate change, Conservation, Ecosystem, Human health, livelihood, Species_

redpajama_set_name: RedPajamaCommonCrawl


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