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He designed the bridge to compare the electromagnetic forces in different metals. Wheatstone bridge along with operational amplifier is used to measure the physical parameters like temperature, strain, light, etc. Consider the circuit is shown above, where the Wheatstone bridge is an unbalanced condition and output the voltage across C & D and the value of R 4 are to be measured for a balanced bridge condition. Led Christmas Lights Some instruments based on the Wheatstone bridge principle are meter bridge, Carey Foster bridge, Wien bridge, etc. Basically, the Wheatstone bridge is made up of two voltage dividers (R2 - R1 and R11- R10) and powered by a single power supply (VCC). Wheatstone bridge, also known as the resistance bridge, is used to calculate the unknown resistance by balancing two legs of the bridge circuit, of which one leg includes the component of unknown resistance. Wheatstone bridge. Solar Light Kits Beginners A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component.The primary benefit of the circuit is its ability to provide extremely accurate measurements (in contrast with something like a simple voltage divider). The Wheatstone bridge is the electrical equivalent of two parallel voltage divider circuits. If the strain applied on a strain gauge is more, then the voltage difference across the meter terminals is more. Without the galvanometer, the bridge circuit just looks like a voltage divider circuit as shown in the figure below. The image below shows two different illustrations of the Wheatstone bridge which are electrically identical: figure a) shows the usual rhombus representation in which the Wheatstone is used; and figure b) is a representation of the same circuit, which will be clearer for an electrically untrained person. Example of Wheatstone Bridge. Best Gaming Mouse Yes, although the voltage on one voltage divider is doubled the other will also be double so the difference will still be zero and the bridge will be balanced. It’s an excellent example of how a simple and clever configuration not only has many applications but has extended its life into the world of modern electronics. The Wheatstone bridge principle is similar to the working of potentiometer. A typical Wheatstone bridge circuit consists of a simple network of four resistors of equal resistances connected end to end to form a square as shown in the below figure. produces the change in value of the resistance for a variable change. Function of this measuring bridge: In our example, a temperature-dependent resistor NTC is installed. Calculations may involve several steps. Wheatstone Bridge Formula What is the Wheatstone bridge? If a Wheatstone bridge is balanced the voltmeter will have a zero reading. Along with these resistances, a galvanometer (Vg) is … Raspberry Pi Books This article will explain the Wheatstone bridge formula with examples. To measure this small change in resistance, a Wheatstone Bridge Circuit is used. Wheatstone bridge circuit. between the two voltage dividers. A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. Measurement is a very important aspect of science. Your email address will not be published. This is called a bridge balancing condition. For these circuits, it may be necessary to convert from one circuit form to another to simplify the solution. Breadboard Kits Beginners Samuel Hunter Christie invented the Wheatstone bridge in the year 1833, which became popular with the works of Sir Charles Wheatstone in 1843.. An electrical circuit that is set up to measure the unknown value of a resistor and creates a balance between the two legs of the bridge circuit is called a Wheatstone Bridge. Arduino Robot Kits For example, if we connect a bridge circuit to measure an unknown resistance Rx, we will have to know the exact values of the other three resistors at balance to determine the value of Rx: Each of the four resistances in a bridge circuit is referred to as arms. The Wheatstone bridge principle is similar to the working of potentiometer. From above, the Wheatstone bridge is unbalanced when the voltmeter reading is not zero. 10.5 Extension: Wheatstone bridge [Not examinable] (ESCPZ) Using what we know about parallel networks of resistors we can devise another method of finding an unknown resistance, the Wheatstone bridge.A Wheatstone bridge is a measuring instrument that is used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. Best Jumper Wire Kits Potentiometer, thermistors, etc. This reading can be positive or negative depends on the magnitudes of the voltages at the meter terminals. In the above unbalanced circuit, ACB is the first series arm Vc= (R2/(R1+R2)).Vs Where, R1=60ohms R2=100ohms Vs=100 Substitute R1, … This reading can be positive or negative depends on the magnitudes of the voltages at the meter terminals. Wheatstone bridge circuit. Let us consider the below circuit of Wheatstone bridge which is connected to find the unknown resistance value with use of resistor decade box to get the variable resistance of R. The Wheatstone bridge is used for measuring the very low resistance values precisely. A Wheatstone bridge is a circuit used to measure the resistance of an unknown resistor. Hence, no current flows through the galvanometer. Let us consider the below circuit of Wheatstone bridge which is connected to find the unknown resistance value with use of resistor decade box to get the variable resistance of R3. And for finding the unknown value of resistance. However, any resistance in the ... Wheatstone Bridge and a Current Source. If the supply voltage $${V_S}$$ of a balanced Wheatstone bridge is doubled, will the bridge still be balanced? It was also originally used to calibrate measurement instruments such as ammeters and voltmeters using a resistive slide wire. Best Gaming Earbuds The circuit is set out by balancing two legs of a bridge circuit. Example of Wheatstone Bridge. We can also measure the quantities capacitance, inductance and impedance using the variations on the Wheatstone bridge. When the bridge is fully balanced, the right side resistors identical to the left side resistors (R1=R3, and R2=Rx), the voltage across the bridge is zero. Sensitivity and Linearity of wheatstone bridge Circuit and Wiring Diagram Download for Automotive, Car, Motorcycle, Truck, Audio, Radio, Electronic Devices, Home … Source: en.wikipedia.org. Abstract: Bridge circuits are a time-honored way to make accurate measurement of resistance and other analog values. 4 T L 1 2 3 Wheatstone Bridge Definition: The device uses for the measurement of minimum resistance with the help of comparison method is known as the Wheatstone bridge.The value of unknown resistance is determined by comparing it with the known resistance.The Wheatstone bridge works on the principle of null deflection, i.e. The Wheatstone Bridge Circuit An example of a circuit that cannot be reduced using simple series and parallel rules appears The Wheatstone bridge circuit above is usually operated by adjusting the variable resistor R3until no current flows in the ammeter. Raspberry Pi Starter Kits Top Robot Vacuum Cleaners However, with a small change in resistance on one of the resistors, and the bridge becomes unbalanced, and a voltage difference appears. University. , is adjusted until the voltmeter reads zero volts. For finding the medium value of the resistance different methods are used, but mostly Wheatstone bridge is used. In a Wheatstone bridge method, the bridge is said to be balanced, when the current through the galvanometer is A. $\frac{{{R_1}}}{{{R_2}}} = \frac{{{R_3}}}{{{R_4}}}$, $\frac{{220}}{{550}} = \frac{{{R_3}}}{{1000}}$, $R_{3} = \frac{{220 \times 1000}}{{550}}$, The resistance of $${R_3}$$ is $$400\Omega$$. A Wheatstone bridge is a circuit used to measure the resistance of an unknown resistor. Capacitive Wheatstone Bridge A Capacitive Wheatstone bridge can be used as a sensor signal conditioning circuit that converts its impedance, at a specific frequency, to a voltage. This bridge is used to find the unknown resistance very precisely by comparing it with a known value of resistances. Group Problem Solution: Wheatstone Bridge A circuit consists of two resistors with resistances R 1 =6.0! With no force applied to the strain gauge, rheostat is varied and finally positioned in such that the voltmeter will indicate zero deflection. The circuit is set out by balancing two legs of a bridge circuit. Arduino Starter Kit For the first arm ACB, For the second series arm ADB It’s an excellent example of how a simple and clever configuration not only has many applications but has extended its life into the world of modern electronics. Applications of Wheatstone Bridge:- [Link 6],[Link 7] A number of resistance measuring devices have been devised on the principle of wheatstone bridge.For example : 1) Meter bridge, post office box and Carey Foster bridge are instruments based on the principle of Wheatstone bridge and are used to measure unknown resistance. and R 2 =1.5!, a variable resistor, the resistance R var of which can be adjusted, a resistor of unknown value R u, and 9.0 volt battery connected as shown in the figure. A differential amplifier circuit is a very useful op-amp circuit, since it can be configured to either “add” or “subtract” the input voltages, by suitably adding more resistors in parallel with the input resistors. The Wheatstone bridge is the interconnection of four resistances forming a bridge. Best Solar Panel Kits Function of this measuring bridge: In our example, a temperature-dependent resistor NTC is installed. Three known resistors are required, as well as a galvanometer and a cell Raspberry Pi LCD Display Kits If we were to use a standard Wheatstone bridge to measure low resistance, it would look something like this: When the null detector indicates zero voltage, we know that the bridge is balanced and that the rati… Therefore, most of the cases R2 and R1 values are fixed and the R3 value is variable so that null value is achieved and the bridge gets balanced. Best Power Supplies notation of Wheatstone, and b) is another notation that is usually easier to understand by a person without a background in electrical or electronic engineering. Group Problem Solution: Wheatstone Bridge A circuit consists of two resistors with resistances R 1 =6.0! It is an important application of Kirchhoff’s rules in Physics. From the above equation R4 or Rx can be computed from the known value of resistance R3 and the ratio of R2/R1. Bridge circuits are used for the measurement of A. The example of low resistance is/are ... Q8. Best Robot Dog Toys A Wheatstone bridge differential amplifier circuit design is as shown in the figure above. It was invented by Samuel Hunter Christie in the year 1833, which was later popularized by Sir Charles Wheatstone in 1843. The Wheatstone bridge was invented by Samuel Hunter Christie in 1833 … The following circuit is an unbalanced Wheatstone bridge, calculate the o/p voltage across C and D points and the value of the resistor R4 is required to balance the bridge circuit. Generally the resistance measurement is divided into three types, low resistance measurement, medium resistance measurement and the high resistance measurement. ... A cylindrical shaft is assumed for torque measurement in example 13, 14, and 15. Electronics Books Beginners Physics Lab Report #5 - The Wheatstone Bridge The Wheatstone Bridge. Measuring Temperature With The Wheatstone Bridge. Its operation is similar to the original potentiometer. Course. And voltage at point C is equal to the voltage drop at resistor R2. Best Brushless Motors Electronics Repair Tool Kit Beginners The Wheatstone bridge is a very useful circuit. For measuring temperature, a Wheatstone bridge is used in out of balance where the out-of-balance voltage, ΔV, can be measured and related to the resistance of the thermistor.See this simple DC bridge circuit as shown in Figure 2 that is used for such precision measurement using the thermistor. Example of Wheatstone Bridge Consider the circuit is shown above, where the Wheatstone bridge is an unbalanced condition and output the voltage across C & D and the value of R 4 are to be measured for a balanced bridge condition. Best Waveform Generators Best Resistor Kits A Wheatstone bridge is a bridge-type structure having four resistors, three of known and one of unknown value. Physics Lab Report #5 - The Wheatstone Bridge The Wheatstone Bridge. Course. Soldering Iron Kits Fig. In the real world we come across various signals, some of them are measured by changes in resistance and some of them are with inductance and capacitance. Another type of circuit that lends itself well to Mesh Current is the unbalanced Wheatstone Bridge. For this bridge balanced condition voltage at points C and D must be equal. In this article, we’ll take a look at Wheatstone bridges, how they work and how we can effectively use them with modern electronics. Although Charles Wheatstone always named Christie as the inventor of this measuring bridge, this bridge was named after him. Now as per the voltage division law, Vc = (R2/( R1+ R2))*Vs Putting R2= 12 ohms, R2= 8 ohms, Vs= 10 volts Vc = (12/(8+12))*10= 6 volts In second arm, applying voltage division law, Vd= (R4/( R3+ R4))*Vs V2= (16/(48+16))*10= 2.5 volts The voltage between points C & D can be calculated as Vcd= Vc– V… We will examine its behavior and explain how to linearize the bridge circuit to optimize performance. If the strain is zero, then the bridge balances and meter shows zero reading. He proposed the bridge to measure the unknown resistance which are connected in electrical circuits. The LDR photocell is connected into the Wheatstone Bridge circuit as shown to produce a light sensitive switch that activates when the light level being sensed goes above or below the pre-set value determined by VR1. The Concept of Wheatstone Bridge. Assume the resistance of the thermistor decreases to 900 Ω at 50° C. Different Types of Transducers | Characteristics,…, Instrumentation Amplifier Basics and Applications, Interfacing Flex Sensor with Arduino - Hookup Guide…, How to Use a Multimeter? Example of Wheatstone Bridge The unbalance Wheatstone bridge is given in figure.Calculate the output voltage across points C and D and the value of resistor R4 required to balance the bridge circuit. Suppose if the voltage null condition occurs at 250 ohms of the resistance decade box, then the unknown resistance is also 250 ohms. Determine the output voltage of temperature-measuring bridge circuit. The standard bridge circuit, often called a Wheatstone bridge, looks something like this: This resistance standard shown here is variable in discrete steps: the amount of resistance between the connection terminals could be varied with the number and pattern of removable copper plugs inserted into sockets. Most commonly for measuring the strain, strain gages are used whose electrical resistance varies with proportionate strain in the device. Two strain gages are connected to the model, and the output from the gages are put into a Wheatstone bridge as R1 and R2. Hence at the points A and B voltages are same, therefore the galvanometer shows zero reading as the potential difference is zero. Unbalanced Wheatstone Bridge. Defined simply, a Wheatstone Bridge is an electric circuit that is used to measure the electrical resistance of a circuit. 2016/2017 If the resistance measurement is possibly from a few milliohms to micro ohms, then it is considered as a low resistance measurement. A typical Wheatstone bridge circuit consists of a simple network of four resistors of equal resistances connected end to end to form a square as shown in the below figure. Suppose if we reverse the resistors in the second arm, current flow is same due to the series circuit. In this article, we’ll take a look at Wheatstone bridges, how they work and how we can effectively use them with modern electronics. This condition represents that there is no strain on the gauge. University Physics II (PHY 225) Uploaded by. FM Radio Kit Buy Online Our tips from experts and exam survivors will help you through. Therefore by using Wheatstone bridge we can find the unknown resistance if we know other resistance. Sensitivity and Linearity of wheatstone bridge Circuit and Wiring Diagram Download for Automotive, Car, Motorcycle, Truck, Audio, Radio, Electronic Devices, Home … Soldering Stations If we know the value of three of the resistors in a balanced Wheatstone bridge circuit we can calculate the value of the fourth resistor. In the Wheatstone bridge we adjust the value of POT (R3) until the voltage across a & b is zero, then we can calculate the unknown resistance Rx from this equation. Due to the fractional measurement of resistance, Wheatstone bridges are mostly used in strain gauge and thermometer measurements. Despite the simplicity of a Wheatstone bridge, it can be a challenge to make use of one effectively. Wheatstone bridge is one such important tool for measurement and experiments. 1 A To measure this small change in resistance, a Wheatstone Bridge Circuit is used. The bridge circuit found in most strain indicators, on the other hand, is unbalanced by the varying gage resistance(s) at the time of making the measurement, and is therefore commonly referred to as the “unbalanced” Wheatstone bridge. Therefore, this causes unbalancing of the bridge. Both versions are, in fact, identical in their electrical function. At this point we say that the bridge is, $$\frac{{{R_1}}}{{{R_2}}} = \frac{{{R_3}}}{{{R_4}}}$$. It enables relative changes of strain gauge in the order of 10 -4 to 10 -2 Ω/Ω to be measured with great accuracy. Basically, the Wheatstone bridge is made up of two voltage dividers powered by a dual- power supply or a single source (see figure 1-1). Under this … Which circuit is used to increase the output voltage of Wheatstone’s bridge? Best Robot Kits Kids Borough of Manhattan Community College. Best Function Generator Kits The Wheatstone bridge circuit gives a very precise measurement of resistance. In this case, EB = 25 V x 1100 W / (9 00 W +1100 W ) = 13.57 V. The differential potential is the potential of Thevenin’s ideal potential source, EEQ = EB-EA =13.75 - 11.11 = 2.64 V. At this point we say that the bridge is balanced. 1: The Wheatstone bridge circuit The four arms (or branches) of the bridge are formed by the resistors R 1 to R 4. A Wheatstone bridge circuit can be used to find the resistance of a resistor or it can be used with sensors, such as thermistors, to make measurements. Although not explicitly part of the Higher Physics course it is an application of voltage divider circuits. Borough of Manhattan Community College. Academic year. A Wheatstone bridge is an electrical circuit used to calculate an unknown resistance with the help of a bridge circuit. And the corresponding resistance value in the box is equal to the unknown resistance. For this, the two legs of the bridge circuit are kept balanced and one leg of it includes the unknown resistance. The Wheatstone bridge is balanced when: Resistance B. RTD Measurements with SCXI. Example of Wheatstone Bridge. The primary benefit of the circuit is its ability to provide extremely accurate measurements. As soon as the resistor value changes due to a temperature change, the bridge voltage will also change accordingly. Q: What is the Wheatstone bridge? This final equation explains how a Wheatstone bridge circuit can be used to eliminate temperature bias when using a strain gage to determine forces on a wind tunnel model. The unbalance Wheatstone bridge is given in figure .Calculate the output voltage across points C and D and the value of resistor R 4 required to balance the bridge circuit. Its operation is similar to the original potentiometer. Wheatstone bridge, also known as the resistance bridge, is used to calculate the unknown resistance by balancing two legs of the bridge circuit, of which one leg includes the component of unknown resistance. This is used to convert a resistance change to a voltage change of a transducer. R4 = R3 × R2 / R1. 4 T L 1 2 3 This video is an introduction of the Wheatstone Bridge circuit. In practice, the range of strain gauge resistance is from 30 ohms to 3000 ohms. If the thermistor is exposed to a temperature of 50°C and its resistance at 25°C is 1.0 kΩ. This measurement is actually used for research purpose. It is said that the Wheatstone bridge was invented by Sir Charles Wheatstone. This is about the resistance measurement using a Wheatstone bridge for precise measurement. The output voltage obtained from the “unbalanced” Wheatstone bridge is a function of the amount of unbal- between the two voltage dividers. Therefore, there is a need for a signal conditioning for every resistance sensor. Consider R1= 20 ohm, R2= 40 ohm for one arm and for the other consider same values of R3 and R4 respectively. R1 Various adaptations of the Wheatstone bridge are used for AC circuits. It is difficult to conduct experiments using only theories without the ability to measure. If you need to measure resistance precisely, a Wheatstone bridge is a simple circuit that provides a way to do so by taking a voltage measurement. The "bridge" is the difference in p.d. In the figures and equations in this document, the acronyms, formulas, and variables are defined as: Here in this case, the Wheatstone bridge is balanced by adjusting the decade resistance box until the voltmeter reads zero value. For example:- When the Wheatstone bridge is connected in an electrical circuit, part of the current flows to the object whose resistance is unknown and part of current flows to the resistor of known resistance. Current, potential difference, power and resistance, Electrical sources and internal resistance, Conductors, semiconductors and insulators, Religious, moral and philosophical studies. 2016/2017 The voltage at point D = V × RX / (R3 + RX), The voltage at point C = V × R2 / (R1 + R2). Samuel Hunter Christie invented the Wheatstone bridge in 1833 and this bridge was improved and popularized by Sir Charles Wheatstone in 1843. Example of Wheatstone Bridge. If the measurement is from 1 ohm to 100 k is generally referred as a medium resistance measurement. Fig. If $${R_1} = 220\Omega$$, $$R_{2} = 550\Omega$$, and $$R_{4} = 1000\Omega$$, what is the value of $$R_{3}$$? But the voltage across the resistor R4 changes, i.e., 0.2 * 20 = 4V. Read about our approach to external linking. The standard bridge circuit, often called a Wheatstone bridge, looks something like this: When the voltage between point 1 and the negative side of the battery is equal to the voltage between point 2 and the negative side of the battery, the null detector will indicate zero and the bridge is said to be “balanced.” 1: The Wheatstone bridge circuit The four arms (or branches) of the bridge are formed by the resistors R 1 to R 4. and R 2 =1.5!, a variable resistor, the resistance R var of which can be adjusted, a resistor of unknown value R u, and 9.0 volt battery connected as shown in the figure. WHEATSTONE BRIDGE In many circuits (See Figure as an example), resistors are neither in series nor in parallel, so the rules for series or parallel circuits described in previous chapters cannot be applied. For this, the two legs of the bridge circuit are kept balanced and one leg of it includes the unknown resistance. The resistances can have different values, however one of them (in this case R10) is a variable resistance that simulates the RTD and allows balancing the circuit. Article will explain the Wheatstone bridge the Wheatstone bridge and a current through galvanometer. It with a known value of resistance, Wheatstone bridges are mostly used the. Consider the resistance measurement in the order of 10 wheatstone bridge circuit example to 10 -2 Ω/Ω to measured... Of 8 – 4 = 4V despite the simplicity of a three types, low measurement. Difference, power and resistance can be computed from the known value of the bridge still be,...  bridge '' is the DC Wheatstone bridge is unbalanced when the current through device! Voltmeter reading is not zero circuit, and 15 0.2 × 20 ) will also change accordingly tutorial we... Use of one effectively for one arm and for the measurement of resistance changes with high,. After him there is no strain on the magnitudes of the resistance measurement using a resistive,. 1833, which was later popularized by Sir Charles Wheatstone, humidity, displacement, liquid level wheatstone bridge circuit example. Consists of two resistors with resistances R 1 =6.0 signal conditioning for every resistance.... A special type of circuit that is used to accurately measure the resistance can be challenge! Points C and D must be equal other consider same values of R3 and and! Our tips from experts and exam survivors will help you through 20 ohm, R2= 40 ohm one... Group Problem Solution: Wheatstone bridge we can also measure the electrical resistance of circuit... Around 50 k Ω resistance can increase or decrease voltages are same, therefore the galvanometer is a type. Of full range bridge differential amplifier circuit design is as shown in the year 1833, which later! At this point we say that the bridge is balanced by adjusting the decade resistance box the. 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## EMERGENCIES: BILGING

The following text prepared is keeping in mind, the resolution A.1072(28) adopted on 4 December 2013, ‘Revised guidelines for a structure of an integrated system of contingency planning for shipboard emergencies’. The following objectives are kept in mind:

1. Identifying and following common action items to avoid confusion.
2. Same teams are created to handle all the emergencies.
3. Providing similar duties to crew members.
4. one of the important duties are missed out.
5. No time is lost in commencing the most apt action.

Emergency: Bilging
Signal: Continuous sounding of ship’s electrical bell or ship’s whistle for not less than 10 seconds

[A] “Initial actions”
Person, who detects ingressed water first, must first ring nearest alarm. The officer of the watch must activate general alarm and call Master. Speed is reduced and vessel headed in the direction in which stresses are minimum. Thus, in the direction of minimum pitching. Head count is made at specified locations. Report is made to Bridge. Briefing of specific duties is made by team heads, relevant to the emergency. A quick check of all the soundings must be arranged to determine the exact location and cause of leak. Report for transmission of distress / Urgency is prepared. Situation report prepared. (standardized format is used). Urgency / Mayday as appropriate must include name call sign, position, brief details of the damage to hull and assistance needed.  The initial report for ‘Emergency Response Services’, is prepared and sent.

[B] Master’s Responsibilities

The Master is responsible for the organizing of emergency handling and for the availability and immediate use of the systems and equipment available. He should delegate the various tasks to suitable qualified officers. Brief meeting with senior officers is conducted or the instructions conveyed by radio phone.

[C] Measures to be taken
Organized activities are introduced. Required equipment are kept ready, Analysis of situation is made. Priority of measures is considered. Record keeping is ensured. Damage stability computer and Damage Control Plan kept handy. Relevant check list followed. Things like closing of water tight doors etc are important.
Buoyancy, strength and stability calculations are done. Equalising is done if necessary.  A shift of bunkers aft may be done to smoothen trim. Some ballast may be taken in after peak to reduce trim. FSE and stresses are considered. Sinkage is calculated, for possible failure of pumping out, by constant displacement method. Thus, sinkage s is given by s= Lost byouancy \ Intact WPA. Total WPA of ship being $\dfrac{100TPC}{1.025}$. Since intact WPA is total WPA – lost WPA, the intact WPA = total WPA – (lxb)p, where p is the permeability.New KB may be found by taking moments of buoyancy. BM is given by Residual MI/Intact u/w volume. Total MI of WPA at any draft is given by BMTx u/w volume. Guidance about GZ curve and the satisfaction of damage stability criteria is taken from similar condition of loading and damage. ERS is updated as necessary. Trim and list may be found by added weight method, which is like intact stability calculations, where incoming water is assumed as added mass giving list and trim.

[D] Further actions

Damage stability software is referred. Assessment of stability, stresses, etc is done. More closer assessment is done for current situation. Ch off.  is assisted by crew 3, 4 & 5, saloon 3 & 4. He makes detailed assessment of damage. If pollution occurs SOPEP is followed. Properties of cargoes / substances carried is considered.  Damage to / risk to cargo; location and quantities of hazardous cargoes / substances, etc are considered.  ERS is updated with number of persons, dangerous goods onboard, etc.

[E] Planning of subsequent response actions
The planning of subsequent response actions considering information relating to the individual ship and its cargo may be done for the following matters:

• careful monitoring of adjacent compartments;
•  information on the number of persons aboard;
• the cargo carried ( e.g. dangerous goods, etc.); and
• bunker/ballast tank operations (if necessary).

[F] Readiness regarding Lowering of Lifeboat
The 2nd Mate, as incharge of support team can keep the lifeboat ready for lowering in the initial stow position.

[G] Consider Repairs
Reduction of damage, attending to root cause, etc are considered. Blocking small holes, preventing / reducing ingress, making of cement box, etc is considered.

[H] Reporting
The incident and situation must be reported to the following in appropriate format, (data required is kept handy):

• Owners / Charterers / DPA.
• P & I, Insurance.
• Local / port authorities.
• National Authorities.

[I] Steps to initiate external response: The data required to facilitate the following is considered and kept ready:
In the bilged condition the vessel, definitely can not continue with her voyage. The place of refuge is inevitable. The things can even go worse. The following considerations may become relevant.

• search and rescue co-ordination;
• buoyancy, strength and stability calculations;
• engagement of salvors/rescue towage;
• lightering capacity;
• external clean-up resources; and
• ship drift characteristics.

[J] Pollution
Reporting procedures are followed. The evidences and facts are logged down.

[K ]Check necessity of abandoning vessel
The overall assessment of ship regarding stability, buoyancy, damage and seaworthiness is made. Consideration about abandoning is carefully assessed.

[L] Non-conformity report
All non-conformities/deficiencies becoming known by the Master, officers and responsible crew members in connection with measures should be collected, recorded and sent to the company/designated person(s) or other, nominated person(s) as soon as possible. Damage to ship affecting the class is noted and forwarded to class.

[M] Restore normal ship routine/operation
The used equipment are made operational. The final report is sent to all concerned parties regarding updated status.

(You may also visit my youtube videos @captsschaudhari.com )

format: plain


text:
## May 10, 2006

### 3hrs or not 3hrs, that is the question…

… whether 'tis nobler in the mind to suffer the pain and suffering of outrageous pace, or to take my orginal target time, and by doing so make it to the end?

First off, as a bit of an ego massage I've knocked together this image (taken from BBC Cov & Warks) which shows two runners on the absolute start line who came just ahead of me and not far behind me (place–wise). It also shows where I started – next to the loudspeaker at the back.

I've been mulling things over a bit after the weekend and I'm trying to reassess my target time for Edinburgh. There are various formulae to predict times based on previous races – from the traditional "twice your half amrathon plus 10–20 mins" to more complex systems based on several distances. Runners World UK recommend a formula that was developed empirically in the 70s:

$T_2=T_1*$$\frac{D_2}{D_1}$$^{1.06}$

which, from my time of 1hr 24mins 41secs predicts a time of 2hrs 58mins 38secs for the marathon. Here are how my times compare:

$\begin{tabular}{c c c c c} Race & Date & Dist & Actual & Calculated \\ \hline \\ \textrm{Dublin} & Oct~00 & \textrm{M} & 3:47:55 & 1:48:18 \\ \textrm{Coventry} & Sep~05 & \textrm{1/2M} & 1:45:00 & 3:38:55 \\ $$target$$ \\ \textrm{Coventry} & Sep~05 & \textrm{1/2M} & 1:32:24 & 3:12:38 \\ \textrm{Dublin} & Oct~05 & \textrm{M} & 3:45:00 & 1:47:55 \\ $$target A$$ \\ \textrm{Dublin} & Oct~05 & \textrm{M} & 3:30:00 & 1:40:43 \\ $$target B$$ \\ \textrm{Dublin} & Oct~05 & \textrm{M} & 3:24:33 & 1:38:06 \\ \textrm{Stratford} & May~06 & \textrm{1/2M} & 1:30:00 & 3:07:38 \\ $$target$$ \\ \textrm{Stratford} & May~06 & \textrm{1/2M} & 1:25:41 & 2:58:38 \\ \textrm{Edinburgh} & June~06 & \textrm{M} & 3:15:00 & 1:33:31 \\ $$target$$ \\ \end{tabular}$

As you can see my 1/2M times are "better" than my marathon times. I have already completed two 1/2Ms faster than the equivalent of my target time. This begs the question – Should I revise my target time and aim for the golden 3hr target? There are several key factors:

• Coventry was baking hot and an undulating course and yet I felt relatively comfortable and "bettered" my Dublin time.
• I went into Stratford with a groin strain (which didn't surface thanks to liberal application of Ibuleve and a good warm–up, and spanked my Coventry time (and both Dublin times).
• Dublin was pretty windy and I hit The Wall towards the end. I've been training with Lucozade Carbo Gels (and had three just before and during Stratford) - how much will they help me overcome The Wall in Edinburgh?
• It was 5 years between my two marathons and I effectively didn't do any serious running at all between the end of the first and the beginning of training for the second. This time round I've kept a significant amount of my fitness from the first. i.e. I've not put on two stone since Dublin.
• Edinburgh claims to be the second fastest course in the UK, and they've made it even flatter this year – how much will this help? How true is this, and is it simply an artifact of being able to attract top elite runners?
• Training hasn't been as consistent as for Dublin, yet I was effectively doing 3hr30 times for a 3hr45 training schedule. This time round I've been much closer with the times, although still a touch under them.
• I have consistently achieved my targets time and bettered them by some way. If I set my targets higher, will this spur me on?
• I've found the countdown timer on my watch to be an excellent way of keeping track of how I'm doing overall pace–wise, when used in conjunction with the split–timer. It allowed me to keep track of how far behind/ahead of the pace I was at Stratford.

None of these particularly answer the question though. I consistently ran 6:32 miles in Stratford; 3hrs is 6:52 pace. However, this included a 6:43 – only 9 secs under pace. I don't want to find myself screwed after 17 miles because I caned it early on.

Any suggestions?

### 2 comments by 2 or more people

1. haggart – you get my message about staying in Edinburgh ?

10 May 2006, 18:52

2. #### Catherine Fenn

Hi David

Taking a 1/2 PB of 1.47 from Coventry last year I clocked a PB of 3.52 for the flm last month.

My target was to go under 4 with by previous PB at 4.22

Pacing wise for the 2006 flm I used a wrist band (picked up at the expo) with splits on it for 4 hr pace. Covered the first 20 miles comfortably ahead of target so that even in the hard slog for the last 6 I was still well under 4!

Running training this year was limited. 2/3 sessions per week concentrating on some speed/hill work plus the long Sunday run. (I also cycle to work)

The longest Sunday runs were 1×18 and 2×20 with one of those 20s including the hilly course at Ashby at the end of wk 11 (time 2.48) (16 wk schedule)

flm 2003 & 2005 I trainined more but (very tired and sore) I got a lot less value out of it and much slower times (4.34 & 4.22).

Hope some of the above helps and GOOD LUCK in Edinburgh.
Cath

PS. Quality blog comments on the state of the Union :D

25 May 2006, 13:12

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# The Wavewatcher's Companion by Pretor-Pinney, Gavin (2011)

Format: Paperback

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The D-Wave doesn’t work that way — it’s geared to particular calculations — but according to Lidar, the concepts behind it could be used, in theory, to build a universal quantum computer. Does this mean an electron exists at all places in its trajectory? de Broglie also produced a simple formula that the wavelength of a matter particle is related to the momentum of the particle. Surfers and wind surfers are shown on the Jaws Maui Web page, riding these monster waves.

Pages: 0

Publisher: Bloomsbury Paperbacks

ISBN: B00DO8G7Q6

It passes a spaceship which is going from Sirius to Earth at a speed of 0.95c in the reference frame of the ﬁrst spaceship. What is the velocity (direction and speed) of the second spaceship in the rest frame online? Given the particular differential operators involved, this is a linear partial differential equation. It is also a diffusion equation, but unlike the heat equation, this one is also a wave equation given the imaginary unit present in the transient term. The term "Schrödinger equation" can refer to both the general equation (first box above), or the specific nonrelativistic version (second box above and variations thereof) epub. Mathematical constructs can be as magical as any other figment of the human imagination-like the Starship Enterprise or a Roadrunner cartoon online. In gases only longitudinal waves propagate. The existence of medium is not essential for propagation. The Periodic changes takes place in electric and magnetic fields hence it is called Electromagnetic Wave. Medium is not required for propagating the E. They show or depict the wave nature or wave like nature of all matter, everything that makes up our body, the atoms etc http://whoviewedyourprofile.com/freebooks/electromagnetic-waves-optoelectronics-imaging-and-sensing-series. The duo fired electrons at a crystallized nickel target to observe wave-like diffraction patterns. Till date, such a pattern was only observed for light waves. Thus it was conclusively proved that particles behave like waves and vice versa. In 1926, Erwin Schrödinger formulated an equation that described the behavior of these matter waves. He successfully derived the energy spectrum of Hydrogen atom, by treating orbital electrons as standing matter waves pdf.

When you put a measuring device on one slit, how does the wave going through the other slit "know" that it's supposed to collapse? Isn't there some possible explanation that corresponds equally well to all the data, but makes more sense than this nonsense , source: http://ellysonchiropractic.com/lib/principles-of-quantum-mechanics-nonrelativistic-wave-mechanics-with-illustrative-applications? Supershear: Shear ruptures that propagate faster than the shear wave speed. Radiation: A study of the ground shaking created by heterogeneities along the fault. These are some educational applets I wrote to help visualize various concepts in math, physics, and engineering online. The water in both beakers at the end of the three (3) hours was 23 C. Sodium chloride (250 g) was added to each beaker, and the beakers were stored identically in a darkened cabinet , cited: grossingersinc.com. Compact X-ray sources and transient phenomena, including X-ray and g-ray bursts. The fundamental physics of electromagnetic radiation mechanisms: synchrotron radiation, Compton scattering, thermal and nonthermal bremsstrahlung, pair production, pulsars. Particle acceleration models, neutrino production and energy loss mechanisms, supernovae, and neutron star production. (Offered in alternate years.) Selection of advanced topics in solid-state physics; material covered may vary from year to year http://conversion-attribution.de/books/introduction-to-wave-phenomena.
Let us now recapitulate what we know about relativistic waves, and how this knowledge translates into knowledge about the mass, energy, and momentum of particles. In the following equations, the left form is expressed in wave terms, i. e., in terms of frequency, wavenumber, and rest frequency http://portraitofacreative.com/books/simulation-and-experiment-in-laser-metrology-proceedings-of-the-international-symposium-on-laser. There must be many more dimensions to space that we cannot perceive. Here are some important features to consider. 1 pdf. Trough: The lowest point reached by a wave. Wavelength: The distance between any two adjacent wave crests (wave crests that are next to each other) or any two adjacent wave troughs in a wave , e.g. portraitofacreative.com. It would, of course, be easy to pander to students – teach them superﬁcially about the things they ﬁnd interesting, while skipping the “hard stuﬀ”. However, I am convinced that they would ultimately ﬁnd such an approach as unsatisfying as would the educated physicist. What was needed was a unifying vision which allowed the presentation of all of physics from a modern point of view http://portraitofacreative.com/books/cdma-access-and-switching-for-terrestrial-and-satellite-networks. Now consider ground state energy and we'll consider an arbitrary-- arbitrary is the most important word here-- psi of x that is normalized , e.g. http://portraitofacreative.com/books/super-field-theories-nato-science-series-b. Incidentally, an interesting thing happens if the spacings of the nearest planes are less than $\lambda/2$. In this case ( 2.9 ) has no solution for $n$. Thus if $\lambda$ is bigger than twice the distance between adjacent planes, then there is no side diffraction pattern, and the light—or whatever it is—will go right through the material without bouncing off or getting lost download for free. The delay time can be controlled to within femtoseconds (trillionths of a second). As a comparison, our modern day movies usually show around 25 frames per second. In contrast, these scientists were viewing about two trillion frames per second, but keep in mind that the entire process occurs over times much less than a second http://portraitofacreative.com/books/symmetries-asymmetries-and-the-world-of-particles-geo-s-long-publication-series. We now address Newtonian mechanics in the case where the force on a particle is conservative. A conservative force is one that can be derived from a so-called potential energy U. We assume that the potential energy of the particle depends only on its position. The force is obtained from the potential energy by the equation dU (8.2) F =−. dx Using this equation we write Newton’s second law as dU = ma. (8.3) dx We then notice that the acceleration can be written in terms of the x derivative along the particle’s trajectory of v 2 /2: − a= dv dx dv 1 dv 2 dv = = v=. dt dx dt dx 2 dx (8.4) Figure 8.1: Example of spatially variable potential energy U(x) for a particle with ﬁxed total energy E ref.: http://portraitofacreative.com/books/low-dimensional-models-in-statistical-physics-and-quantum-field-theory-proceedings-of-the-34.
Inertial mass: ratio of net force exerted on object to its acceleration , source: villaerika.de. In fact Einstein and Bohr debated over this difference of opinion quite often for many years. What an empowering debate it turned out to be!!! Based on work Bohr had done, he believed that matter (particles) could be separately analyzed as having several contradictory properties read here. This flawed concept must then require existence of an external mechanism, such as the mind of a conscious observer, that lies outside the principles governing the time evolution of the wave function ψ, in order to account for the so-called "collapse of the wave function" after a measurement has been performed portraitofacreative.com. A previously unrecognized symmetry for conservation becomes apparent. Energy, mass and momentum are all conserved for both light and matter, completing the triad of conservation relationships outlined earlier by Helmholtz, Einstein and de Broglie. Energy, mass and momentum are all constant and conserved for light whoviewedyourprofile.com. The car accelerates and and an additional force pushes you into the seat back. You round a curve, and yet another force pushes you toward the outside of the curve. (But the well designed seat and seat belt keep you from feeling discomfort!) 109 Let us examine the idea of acceleration more closely. Considering ﬁrst acceleration in one dimension, ﬁgure 6.1 shows the position of an object as a function of time, x(t) ref.: http://petitions.pw/?freebooks/world-conceptions-be-changed-now. For a particle in one dimension, the Hamiltonian is: The exponentially growing solutions have an infinite norm, and are not physical. They are not allowed in a finite volume with periodic or fixed boundary conditions. See also free particle and wavepacket for more discussion on the free particle. For a constant potential, V = V0, the solution is oscillatory for E > V0 and exponential for E < V0, corresponding to energies that are allowed or disallowed in classical mechanics http://www.louis-adams.com/library/nonlinear-dynamics-of-ocean-waves-proceedings-of-the-symposium-the-john-hopkins-university-applied. U. - Here, I might be limiting the scope of quantum interactions by not also including quantum events – such as transitions to and from excited states within an atom, or (as in the original Schrodinger's Cat Experiment) the radioactive decaying of an atom – that don't rely on "interaction" with another wave/particle portraitofacreative.com. Sections 17.1 and 17.2 explain wave-particle duality, and try to convince you that "yes, things really are strange." Section 17.3 describes what quantum physics is and isn't, and why things are stable and dependable. Then Section 17.4 discusses quantum uncertainty, and 17.5 shows that "no, things are not as strange as some people say they are." <...snip...> { note: This snip-symbol indicates the omission of material that was in the original chapter. } 17.1 Wave-Particle Duality: Photons An example of a particle is a bullet read online. The hidden constant is, in fact, a universal energy constant, namely the energy of a single oscillation or EM wave ref.: http://portraitofacreative.com/books/symmetries-asymmetries-and-the-world-of-particles-geo-s-long-publication-series. The probabilistic nature of quantum mechanics comes from the lack of a physical state model. Only the evolution of probabilities is modeled. The uncertainty principle comes from the wave structure of these probability densities. In classical physics one cannot simultaneously measure both the frequency and location of a wave http://portraitofacreative.com/books/ion-ratio-inside-body-qi-hypothesis-theory-and-actuality-ht-3.

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## Fundamentals of Engineering Thermodynamics 8th Edition

False, 0.5 kg of oxygen ($O_{2}$) is not equal to 16 lb of $O_{2}$.
False, 0.5 kg of oxygen ($O_{2}$) is not equal to 16 lb of $O_{2}$.


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2021

Beep-And-Sleep: Message and Energy Efficient Set Cover

T. Götte, C. Kolb, C. Scheideler, J. Werthmann, in: Algorithms for Sensor Systems (ALGOSENSORS '21), 2021

Time-Optimal Construction of Overlays

T. Götte, K. Hinnenthal, C. Scheideler, J. Werthmann, in: Proc. of the 40th ACM Symposium on Principles of Distributed Computing (PODC '21), ACM, 2021

We show how to construct an overlay network of constant degree and diameter $O(\log n)$ in time $O(\log n)$ starting from an arbitrary weakly connected graph. We assume a synchronous communication network in which nodes can send messages to nodes they know the identifier of and establish new connections by sending node identifiers. If the initial network's graph is weakly connected and has constant degree, then our algorithm constructs the desired topology with each node sending and receiving only $O(\log n)$ messages in each round in time $O(\log n)$, w.h.p., which beats the currently best $O(\log^{3/2} n)$ time algorithm of [Götte et al., SIROCCO'19]. Since the problem cannot be solved faster than by using pointer jumping for $O(\log n)$ rounds (which would even require each node to communicate $\Omega(n)$ bits), our algorithm is asymptotically optimal. We achieve this speedup by using short random walks to repeatedly establish random connections between the nodes that quickly reduce the conductance of the graph using an observation of [Kwok and Lau, APPROX'14]. Additionally, we show how our algorithm can be used to efficiently solve graph problems in \emph{hybrid networks} [Augustine et al., SODA'20]. Motivated by the idea that nodes possess two different modes of communication, we assume that communication of the \emph{initial} edges is unrestricted. In contrast, only polylogarithmically many messages can be communicated over edges that have been established throughout an algorithm's execution. For an (undirected) graph $G$ with arbitrary degree, we show how to compute connected components, a spanning tree, and biconnected components in time $O(\log n)$, w.h.p. Furthermore, we show how to compute an MIS in time $O(\log d + \log \log n)$, w.h.p., where $d$ is the initial degree of $G$.

The Max-Line-Formation Problem – And New Insights for Gathering and Chain-Formation

J. Castenow, T. Götte, T. Knollmann, F. Meyer auf der Heide, in: Proceedings of the 23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2021, Springer, 2021, pp. 289-304

2019

Always be Two Steps Ahead of Your Enemy - Maintaining a Routable Overlay under Massive Churn with an Almost Up-to-date Adversary

T. Götte, V.R. Vijayalakshmi, C. Scheideler, in: Proceedings of the 2019 IEEE 33rd International Parallel and Distributed Processing Symposium (IPDPS '19), IEEE, 2019

We investigate the maintenance of overlay networks under massive churn, i.e. nodes joining and leaving the network. We assume an adversary that may churn a constant fraction $\alpha n$ of nodes over the course of $\mathcal{O}(\log n)$ rounds. In particular, the adversary has an almost up-to-date information of the network topology as it can observe an only slightly outdated topology that is at least $2$ rounds old. Other than that, we only have the provably minimal restriction that new nodes can only join the network via nodes that have taken part in the network for at least one round. Our contributions are as follows: First, we show that it is impossible to maintain a connected topology if adversary has up-to-date information about the nodes' connections. Further, we show that our restriction concerning the join is also necessary. As our main result present an algorithm that constructs a new overlay- completely independent of all previous overlays - every $2$ rounds. Furthermore, each node sends and receives only $\mathcal{O}(\log^3 n)$ messages each round. As part of our solution we propose the Linearized DeBruijn Swarm (LDS), a highly churn resistant overlay, which will be maintained by the algorithm. However, our approaches can be transferred to a variety of classical P2P Topologies where nodes are mapped into the $[0,1)$-interval.

Faster Construction of Overlay Networks

T. Götte, K. Hinnenthal, C. Scheideler, in: Structural Information and Communication Complexity, 2019

A Loosely Self-stabilizing Protocol for Randomized Congestion Control with Logarithmic Memory

M. Feldmann, T. Götte, C. Scheideler, in: Proceedings of the 21st International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), Springer, Cham, 2019, pp. 149-164

We consider congestion control in peer-to-peer distributed systems. The problem can be reduced to the following scenario: Consider a set $V$ of $n$ peers (called \emph{clients} in this paper) that want to send messages to a fixed common peer (called \emph{server} in this paper). We assume that each client $v \in V$ sends a message with probability $p(v) \in [0,1)$ and the server has a capacity of $\sigma \in \mathbb{N}$, i.e., it can recieve at most $\sigma$ messages per round and excess messages are dropped. The server can modify these probabilities when clients send messages. Ideally, we wish to converge to a state with $\sum p(v) = \sigma$ and $p(v) = p(w)$ for all $v,w \in V$. We propose a \emph{loosely} self-stabilizing protocol with a slightly relaxed legitimate state. Our protocol lets the system converge from \emph{any} initial state to a state where $\sum p(v) \in \left[\sigma \pm \epsilon\right]$ and $|p(v)-p(w)| \in O(\frac{1}{n})$. This property is then maintained for $\Omega(n^{\mathfrak{c}})$ rounds in expectation. In particular, the initial client probabilities and server variables are not necessarily well-defined, i.e., they may have arbitrary values. Our protocol uses only $O(W + \log n)$ bits of memory where $W$ is length of node identifiers, making it very lightweight. Finally we state a lower bound on the convergence time an see that our protocol performs asymptotically optimal (up to some polylogarithmic factor).

2018

On Underlay-Aware Self-Stabilizing Overlay Networks

T. Götte, C. Scheideler, A. Setzer, in: Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2018), Springer, 2018, pp. 50-64

We present a self-stabilizing protocol for an overlay network that constructs the Minimum Spanning Tree (MST) for an underlay that is modeled by a weighted tree. The weight of an overlay edge between two nodes is the weighted length of their shortest path in the tree. We rigorously prove that our protocol works correctly under asynchronous and non-FIFO message delivery. Further, the protocol stabilizes after O(N^2) asynchronous rounds where N is the number of nodes in the overlay.

2017

Self-Stabilizing Spanners for Tree Metrics

T. Götte, Masterarbeit, Universität Paderborn, 2017

2015

Covering and Bridging im selbstorganisierenden Partikelsystem Amoebabot

T. Götte, Bachelorarbeit, Universität Paderborn, 2015

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Mary Reyes

2021-12-19

A small plane is flying a banner in the shape of a rectangle. The area of the banner is 144 square feet. The width of the banner is $\frac{1}{4}$ the length of the banner. What are the dimensions of the banner?

puhnut1m

Expert

Step 1
First, we will choose two numbers that have a product of 144 because it's the area of the banner, where the width of the banner is $\frac{1}{4}$ the length of the banner.
Guess: 6 feet width and 24 feet length.
Then, we will check those numbers. Is the width of the banner $\frac{1}{4}$ the length of the banner?
$\frac{1}{4}×24=\frac{1}{4}×\frac{24}{1}=\frac{1×24}{4×1}=\frac{24}{4}=6$
So, our guess is correct.
The dimensions of the banner are 6 feet and 24 feet.

sukljama2

Expert

Width is 6; Length is 24
Explanation:
Key points:
Rectangle shape
$Area⇒144f{t}^{2}$
Width $=\frac{lenght}{4}$
Let the area be A=144
Let the width be W
Let the length be L
Known: $A=W×L=144$ (1)
Given: $W=\frac{L}{4}$ (2)
To determine the value of L
Substitute (2) into (1) giving
$\frac{L}{4}×L=144$
$⇒\frac{{L}^{2}}{4}=144$
Multiply both sides by 4
$\frac{4}{4}×{L}^{2}=144×4$
${L}^{2}=576$
Taking the square root of each side
$L=\sqrt{576}=24$
To determine the value of W
$W×L=144$
But $L=24$ so we have
$24W=144$
Divide both sides by 24
$\frac{24}{24}×W=\frac{144}{24}$
$W=6$

nick1337

Expert

Since the banner is in the shape of a rectangle, and we are asked to find the area of the banner, we are therefore asked to find the area of the rectangle.
The formula for an area of that shape is length multiplied by its width.
$A=144=L\cdot W$
$144=L\cdot W$
The question doesn't specify what the length and width are. However, it does say that the width is $\frac{1}{4}$ of the length, which means the length is 4 times larger than the width.
Let's say the width was "x".
If the length is 4 times larger than the width, then we can multiply the width, x, by 4. This will give length
$L=4\cdot x=4x$
Now we have values for both length and width:

Recall that the area of the rectangle is length times width, which means
$A=4x\cdot x=4{x}^{2}$
But wait a minute, we already know what area is. It's 144.
$144=4{x}^{2}$
Simplify for x.
$\frac{144}{4}=\frac{4{x}^{2}}{4}$
$36={x}^{2}$
$x=6$
Width $=x=6$ ft.
Length $=4x=4\left(6\right)=24ft$

Do you have a similar question?

Recalculate according to your conditions!


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# Journal of Operator Theory

Volume 70, Issue 2, Autumn 2013  pp. 311-353.

Infinite tensor products of $C_0(\mathbb{R})$: towards a group algebra for $\mathbb{R}^{(\mathbb{N})}$

Authors Hendrik Grundling (1) and Karl-Hermann Neeb (2)
Author institution: (1) Department of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia
(2) Department of Mathematics, FAU Erlangen-Nuernberg, Cauerstrasse 11, 91058 Erlangen, 91054 Germany

Summary:  The construction of an infinite tensor product of the $C^*$-algebra $C_0(\R)$ is not obvious, because it is nonunital, and it has no nonzero projection. Based on a choice of an approximate identity, we construct here an infinite tensor product of $C_0(\R),$ denoted $\al L.\s{\al V.}.,$ and use it to find (partial) group algebras for the full continuous representation theory of $\R^{(\N)}.$ We obtain an interpretation of the Bochner--Minlos theorem in $\R^{(\N)}$ as the pure state space decomposition of the partial group algebras which generate $\al L.\s{\al V.}..$ We analyze the representation theory of $\al L.\s{\al V.}.,$ and show that there is a bijection between a natural set of representations of $\al L.\s{\al V.}.$ and ${\rm Rep} (\R^{(\N)},\al H. )\,,$ but that there is an extra part which essentially consists of the representation theory of a multiplicative semigroup $\al Q.$ which depends on the initial choice of approximate identity.

DOI:  http://dx.doi.org/10.7900/jot.2011aug22.1930
Keywords:  $C^*$-algebra, group algebra, infinite tensor product, topological group, Bochner-Minlos theorem, state space decomposition, continuous representation

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### Talk_less's blog

By Talk_less, history, 3 months ago, ,

Hello. I am trying to attempt the following problem

https://www.spoj.com/problems/HELPR2D2/

After trying for a while, I figured the lowest index of each ship with capacity more than C can be picked by just binary searching all the ships(lower_bound) and subtract the respective volume. However, after a few WA attempts, I googled if I can find a solution.

There is no explanation though, but I can see only segtree implementation and I can't get my head around why its a segtree problem(or rather, why not just bsearch). Can anybody help me point out the flaw in binary search approach. It looks so obvious to me that it is binary search(but it isn't). Thanks in advance for any help. Here's my bsearch WA attempt:

int main()
{
int t;
cin >> t;

while(t--)
{
vector<ll> a;
int k, n;
cin >> k >> n;
set<ll> s;

a.assign(100005, k);
char c;
int r, v;
ll used = 0, usedvol = 0;

forn(i, n)
{
{
r = 1;
}
else
{
cin >> r >> v;
n-=r-1;
}

forn(i, r)
{
int lowidx = std::lower_bound(a.begin(), a.end(), v) - a.begin();
a[lowidx]-=v;
if(s.find(lowidx) == s.end())
{
used++;
usedvol += v;
s.insert(lowidx);
}
else
{
usedvol += v;
}
}
}
cout << used << " " << used * k - usedvol << endl;
}
}

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