Mastering physics what is the magic number




















I read that throught virtual environment, i can run windows. However, I dont like to download "hacked" progs. I do like to do it through linux. What options exist? Here is link for similar problem. Show 4 more comments. Active Oldest Votes. I assume there's a confusion between disk partition table and partition with a file system. Improve this answer. Ginnungagap Ginnungagap 5 5 bronze badges. Not, exactly. Gparted shows a disk, with a single partition.

There were not multiple partitions. Now, I formatted the disk to ext4. So, bye bye ntfs problem! Just because your partition table contains a single partition does not mean it is not a partition table. Whether ext4, NTFS, btrfs, ZFS or any other file system, unless you format the disk directly which I'm not sure you can do from GParted , you will still have a partition table with a partition with a file system. When an assignment question requires that you answer by drawing vectors or moments, you will see the following buttons.

To draw a new vector, click and select the label for the vector that you want to draw. You can draw the vector by clicking on the start point and dragging your mouse to the end point. To edit an existing vector, click to select either the vector, its start point, or its end point. Drag the selected vector or point to a new location. Some questions will ask you to mark moments.

To deselect a vector or moment, click on any empty area of the workspace. To view the sum of all the vectors in your drawing, click. This option is not available in every problem. To delete a selected vector or moment, click. To delete using your keyboard, press Delete or Backspace after selecting a vector or moment. To view the information about or change the properties of a vector or moment, select the vector or moment, which will display properties if they are needed for the problem such as:.

Here, you can also change a label by selecting another vector or moment. To reset your vectors or moments to the most recently submitted answer restart , click. Part A Every morning Ann walks her dog through the park, shown as a green square on the diagram below.

They start at point 1, walk one block up the street, take a turn at the corner labeled 2, and walk diagonally through the park to point 3. To return home, they walk two blocks down the street and turn right at the corner labeled 4.

Represent each segment of Anna's walk with a vector. The vectors should start and end at the centers of the red dots located on the image. Draw Ann's path. Represent Ann's walk with a vector of length 80 meters. Draw the vector starting at point 1. The length given in the display is in meters. Part C The diagram below shows a force being applied on a beam. Mark the direction of moment at the fulcrum by clicking on the dot indicated by M. Part A You are starting a new item and after reading the first part you realize you have no idea how to go about answering it.

What should you do? You have been working on an item for a while and after a few missteps you've come up with an answer. Select all that apply. Check for any hints that address the part of the calculation you're unsure about. Submit your answer and then adjust it according to any feedback you receive. Return to the question after you've spoken with an instructor or classmate. How would you enter this number into the answer box?

Enter your answer in kilograms using three significant figures. Note that the units are provided for you to the right of the answer box. You may use the scientific notation template to enter your answer, or type the following: 9.

Part D A friend in your class tells you that she never uses hints when doing her Mastering homework. She says that she finds the hints helpful, but when the hint asks another question it increases the chance that her score on the problem will go down. She feels like it isn't worth the risk. You reassure her that there is nothing to fear about opening a hint that asks a question.

Which of the following are good reasons for your friend not to worry? The only way to lose additional partial credit on a hint is by using the "Request Answer" button or entering incorrect answers.

Leaving the question blank will not cost you any credit. Getting the correct answer to the question in a hint actually gives you some partial credit, even if you still can't answer the original question. As an incentive for thinking hard about the problem, your instructor may choose to apply a small hint penalty, but this penalty is the same whether the hint simply gives information or asks another question.

Some Mastering courses include Dynamic Study Modules. To learn more, watch the video, Getting Started: Dynamic Study Modules, and answer the questions below. Assess what a student already knows, and where he or she may want to focus additional study.

Give students real-life applications of the concepts they are currently learning in class. Normalize student learning so the teacher knows what to focus on in lecture. Allow students to collaborate with each other on assignments in Mastering. Previously signing in from a desktop, if using DSM on the mobile app. Enrollment in a course that uses Mastering with Dynamic Study Modules.

Mindset is an idea proposed by Stanford University psychologist Carol Dweck based on her research in motivation and development. According to Dweck, people generally have a tendency to think with one of two different mindsets: a fixed mindset or a growth mindset.

As you start this semester, it can be useful to think about some ideas and strategies that will help you to succeed. In these materials, we will describe some ideas about motivation, based on cutting-edge research, and offer some suggestions for how to get the most out of Mastering and your course. Part A Which of the following describes a growth mindset, as opposed to a fixed mindset? Challenging yourself by persisting longer with problems helps to grow your mental muscle. Believing your talents, abilities, and intelligence can be developed in different ways.

Having a fixed mindset in some ways, and a growth mindset in others. The ability to make new and stronger connections between the neurons in our brain as we learn. Always wear protective clothing, appropriate gloves, and eye gear when in the chemistry lab.

Part C How do students with a growth mindset see their mistakes? Part D How do you develop a growth mindset and embrace your mistakes? Part E Why is the word "yet" powerful in developing a growth mindset? It encourages you to continue along your learning journey, as you have not yet reached the final destination. It encourages you to skip steps necessary to learn difficult concepts quickly.

It encourages you to stop trying when you fail because you are not smart enough. Part G How do people with a growth mindset view and respond to challenges? They see challenges as opportunities to learn and push their abilities.

Some problems in MasteringPhysics require answers in the form of a single vector or an expression involving multiple vectors. This problem will show you how to enter vector answers in MasteringPhysics.

One common way of expressing vectors is in terms of their components. When a problem in MasteringPhysics requires a vector answer in component form, the answer instructions will typically read something like "Enter your answer as a pair of vector components, separated by a comma. The surrounding parentheses should not be entered. Enter your answer as a pair of vector components, separated by a comma. You should not enter any parentheses.

Unit vectors As the name suggests, unit vectors are vectors of unit length 1. If the reason for this is presently unclear, don't worry; you will learn more about vectors in class.

Here we just want to be sure you know how to enter them in MasteringPhysics. You received 13 out of a possible total of 13 points.

Open navigation menu. Close suggestions Search Search. User Settings. Skip carousel. Carousel Previous. Carousel Next. What is Scribd? Intro To Mastering Physics. Uploaded by Siva Ram. Document Information click to expand document information Description: helpful.

Original Title Intro to Mastering Physics. Did you find this document useful? Is this content inappropriate? Report this Document. Description: helpful. Flag for inappropriate content. Download now. Original Title: Intro to Mastering Physics. Related titles. Carousel Previous Carousel Next. Jump to Page. Search inside document. Grading Policy A message from your instructor A Welcome to Mastering! The Battle Frontier. Afghan Jerseys. Dhapu and the Call Stack.

Yalins Dictionary. Mad King. Lost in a Grid. Chef and Dishes. Chaapu and Matisse. Bomb Squad. Dexter is drunk. Holy Sequence. Save Sita. Robo Vision. Sadiq On a Date. Stacks Pattern. Women in Engg. The Hacker. Largest Number. A game with primes. Indhiran II. Count Distinct Sets. Nobita and the Alien Dictionary.

Just another episode in Johnny Test. Desolation of Smaug. Homework For A Trip. Dinner With Friends. The Imperfect Sheet. Recharge on V-Day. The Book of Love. X and Y. Builder Tools Weasley Wizard Wheezes. Battle of Black Water. The Rich Rice Trader. The Bird in a Nest. Hightech Flour Mill. Charlie and the Chocolate Factory.

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Playing with Combinatorics. Board Game. Birthday Game. Decode the messages. DJ and Triangles. Tring Tring!!! The Machine. Cutting the largest piece. Gopal and his Crying Sons. Gopal and his Task. Will India reach the final. Gandalf the Grey. Shriraj and Debt. Shriraj and Maze. Shriraj and Points. Valid phone number. Churu and his Sequence.

Churu Criteria for stability of Imaginary Gases. Encrypted Message. Counting Stars. The maximum area. Alphabets and Utthaan. The count of pattern. Can the Problem be Solved. Cheese Fight. K Repeater.

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Chef in a new city. Try Harder. Land Mines of Byteland. Attack on Titans. Capt sparrow. Cake Shop. Crisis of infinite universes. Warehouse Management. Counting on Tree. Walcott and Equivalence Relation. Odd Game. Cman and Candies. Palindromic Substrings. Anxious Aritra. Color them all. Balance the see-saw. Make them work. King and the roads. Find the cities. Raiders of the Rectangular Pool. Game of Cards. RK and Iron Man. Square Bullseye. Anuj and his Set. Chef visits USA. Find the Grid.

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Rescuing Vanessa yet again! Breaking the Lock. No Do not solve me, I am hard! Raju and his safes. I have got the power! Reverse Asignment. Express differently. Viru and his Unique Series. Trumph and Maze. Election Commision. Maximize Performance. Geek Room. Queen of Andals. Revenge of Cersei. Miraculous Circle. Special Bonds. Magic shows strong evidence of heritability, with familial aggregation and concordance in twins.

Evidence suggests magical ability to be a quantitative trait. Specific magical skills, notably being able to speak to snakes, predict the future, and change hair colour, all seem heritable. A multilocus model with a dominant gene for magic might exist, controlled epistatically by one or more loci, possibly recessive in nature.

Magical enhancers regulating gene expressionmay be involved, combined with mutations at specific genes implicated in speech and hair colour such as FOXP2 and MCR1. Children's and adults' reactions to magical and ordinary suggestion: are suggestibility and magical thinking psychologically close relatives? In Experiment 1, 6- and 9-year-old children and adults were asked to imagine various types of objects.

The experimenter then attempted to change the image of those objects in participants' minds by either suggesting that the objects may change against the participants' will, or by asking participants to change the objects as a favor to the experimenter. Two types of suggestive causation were employed: Magical -suggestion a magic spell was cast with the aim of changing the imagined objects and ordinary-suggestion participants were told that the objects in their minds could alter against their will.

Ordinary-suggestion was as effective as magical -suggestion in changing the participants' imagined objects. For adults, a direct request for compliance produced a stronger effect than did magical suggestion. This effect was not found in children. In Experiment 2, the two types of suggestion were tested on an alternative type of imagined objects.

Adult participants were asked to imagine their futures. It was then proposed that a a magic spell could be cast on their futures with the aim of changing them either for the worse or for the better magical -suggestion , or b changing a numerical pattern on a computer screen could change their futures ordinary-suggestion.

All participants denied that changing a numerical pattern on a computer screen could affect their lives, yet in their actions they demonstrated an element of belief in this possibility. As in Experiment 1, in Experiment 2 ordinary suggestion was as effective as magical suggestion. The hypothesis of an historic contiguity between magical causality and ordinary suggestion is discussed.

George Miller's magical number of immediate memory in retrospect: Observations on the faltering progression of science. Though influential in several ways, for about 40 years it was oddly followed by rather little research on the numerical limit of capacity in working memory, or on the relation between 3 potentially related phenomena that Miller described.

Given that the article was written in a humorous tone and was framed around a tongue-in-cheek premise persecution by an integer , I argue that it may have inadvertently stymied progress on these topics as researchers attempted to avoid ridicule. This commentary relates some correspondence with Miller on his article and concludes with a call to avoid self-censorship of our less conventional ideas. Electronic structures of Al-Si clusters and the magic number structure Al8Si4.

The results show that the close-packed structures are preferable in energy for Al-Si clusters and in most cases there exist a few isomers with close energies. The valence molecular orbitals, the orbital level structures and the electron localisation function ELF consistently demonstrate that the electronic structures of Al-Si clusters can be described by the jellium model. Al8Si4 corresponds to a magic number structure with pronounced stability and large energy gap; the 40 valence electrons form closed 1S21P61DS21FP6 shells.

The Magic Breakfast project provided schools with support and resources to offer a free, universal, before-school breakfast club, including to all Year 2 and Year 6 pupils. The aim of the project was to improve attainment outcomes by increasing the number of children who ate a healthy breakfast. The schools in the project were schools in…. Though influential in several ways, for about 40 years it was oddly followed by rather little research on the numerical limit of capacity in working memory, or on the relation between three potentially related phenomena that Miller described.

Characterization of completely k- magic regular graphs. In this paper, we characterize all completely k- magic regular graphs. The magic words: Using computers to uncover mental associations for use in magic trick design. The use of computational systems to aid in the design of magic tricks has been previously explored.

Here further steps are taken in this direction, introducing the use of computer technology as a natural language data sourcing and processing tool for magic trick design purposes.

Crowd sourcing of psychological concepts is investigated; further, the role of human associative memory and its exploitation in magical effects is explored. A new trick is developed and evaluated: a physical card trick partially designed by a computational system configured to search for and explore conceptual spaces readily understood by spectators. Different conditions of magical thinking have been analyzed. A formation of the proportion "realistic thinking - magical thinking" in paranoid schizophrenia has been discussed and the characteristic features of magical thinking in schizophrenia have been indicated.

The Magnetics Information Consortium MagIC is a multi-user facility to establish and maintain a state-of-the-art relational database and digital archive for rock and paleomagnetic data. The goal of MagIC is to make such data generally available and to provide an information technology infrastructure for these and other research-oriented databases run by the international community.

As its name implies, MagIC will not be restricted to paleomagnetic or rock magnetic data only, although MagIC will focus on these kinds of information during its setup phase. MagIC will be hosted under EarthRef. The MagIC database will store all measurements and their derived properties for studies of paleomagnetic directions inclination, declination and their intensities, and for rock magnetic experiments hysteresis, remanence, susceptibility, anisotropy.

Compact Magic -T using microstrip-slotline transitions. The design of a compact low-loss Magic -T is described. The planar Magic -T incorporates a compact microstrip-slotline tee junction and small microstrip-slotline transition area to reduce slotline radiation. Magical Landscapes: Two Love Stories. Introduces two books about magic , one a collection of essays "Ex Libris: Confessions of a Common Reader," which describes the author's inherited lifelong passion for books and reading; and the other a novel, "Mangos, Bananas and Coconuts: A Cuban Love Story," which tells a story of love and magic that seems both real and….

Emotional salience, emotional awareness, peculiar beliefs, and magical thinking. Study 1 examined belief that a baseball team was cursed. Study 2 measured magical thinking using a procedure developed by P. Rozin and C. Nemeroff In both studies, peculiar beliefs and magical thinking were associated with Salience x Attention x Clarity interactions.

Among individuals for whom the objects of the belief- magical thinking were highly emotionally salient and who had high levels of attention to emotion, higher levels of emotional clarity were associated with increased peculiar beliefs- magical thinking.

In contrast, among individuals for whom the objects of the belief- magical thinking were not emotionally salient and who had high levels of attention to emotion, higher levels of emotional clarity were associated with diminished peculiar beliefs- magical thinking. Magical ideation modulates spatial behavior. Previous research has found that animals as well as persons with psychotic disorders preferentially orient away from the cerebral hemisphere with the more active dopamine system.

This study investigated the modulation of spatial behavior by a mode of thinking reminiscent of the positive symptoms of psychosis. In a non-treatment-seeking sample of healthy volunteers 20 women and 16 men , the authors assessed the lateral biases in turning and veering behavior and in line bisection as a function of their magical ideation, that is, a mild form of schizotypy. Across tasks, pronounced magical ideation was associated with reduced right-sided orientation preferences.

This finding suggests a relative hyperdopaminergia of the right hemisphere as the biological basis of magical ideation. Ground-state properties of neutron magic nuclei. Our present investigation includes deformation, binding energy, two-proton separation energy, single-particle energy, rms radii along with proton and neutron density profiles, etc. Several of these results are compared with the results calculated using nonrelativistic approach Skyrme—Hartree—Fock method along with available experimental data and indeed they are found with excellent agreement.

In addition, the possible locations of themore » proton and neutron drip-lines, the Z, N values for the new shell closures, disappearance of traditional shell closures as suggested by the detailed analyzes of results are also discussed in detail. Garden Gnomes: Magical or Tacky? Garden gnomes: magical or tacky? Well, art is in the eye of the beholder, and for the author's advanced seventh-grade art class, garden gnomes are magical.

Gnomes have a very long history, dating back to medieval times. A fairytale describes them as brownie-like creatures that are nocturnal helpers. In this article, the author describes how her…. Magic Tool Suite for Windows. It uses the standard Windows Help so it is pretty self-explanatory. You can use the panel to the left to scan through Tirnc and Space Go to Part 4.

Spatial Extensions Go to Part 5. Properties Go to Part 6. Algorithms Go. Airbag Trail Dubbed ' Magic Carpet'. The drag mark was made after the rover landed and its airbags were deflated and retracted. Scientists have dubbed the region the ' Magic Carpet' after a crumpled portion of the soil that appears to have been peeled away lower left side of the drag mark.

Rocks were also dragged by the airbags, leaving impressions and 'bow waves' in the soil. The mission team plans to drive the rover over to this site to look for additional clues about the composition of the martian soil. This image was taken by Spirit's panoramic camera. This extreme close-up image see insets above highlights the martian feature that scientists have named ' Magic Carpet' because of its resemblance to a crumpled carpet fold.

Scientists think the soil here may have detached from its underlying layer, possibly due to interaction with the Mars Exploration Rover Spirit's airbag after landing. This image was taken on Mars by the rover's panoramic camera. Organ transplantation and magical thinking. Organ transplantation can provide important treatment benefits in a variety of situations.

While a number of live donor procedures are now possible, procurement of organs from dead donors remains the mainstay of transplant programmes. However, cadaveric donation rates remain much lower than anticipated, and some patients who receive organs struggle to adapt to their new body.

The reasons for this are not entirely explained by rational or logical means. This paper uses concepts drawn from magical thinking to try to explain some of the less apparent issues at play within the process of cadaveric organ transplantation, including both the donation and receiving of organs.

Three themes are explored as potentially relevant: superstitions and rituals around death and the dead body, incorporation and the meanings attached to the transplanted organ, and survivor guilt.

All three are shown to be relevant for some part of the transplantation process in at least a minority of cases. It is therefore suggested that focusing not only on the logical and scientific, but also on the ambiguous and magical may enhance the organ donation process and thus increase donation rates and the psychological adjustment of transplant recipients.

Religious and magical ways of healing have been known and practiced since the very beginning of human history. In the present article, the Byzantine philosophical, cultural, historical and "methodological" aspects of this way of healing are discussed. The article outlines the development of magic healing in Byzantium from the 4th to the 15th century. During this period magical therapy included the cult of patron saints--listed by the author--and pleading for divine intervention as well.

The activity of "anargyroi" and the use of magical objects and amulets is also discussed in detail. Exorcism was also a part of religious therapy both against psychical and somatical diseases. In early Christianity, and especially in Byzantium the devil or other demons were also supposed to cause various somatical or psychical illnesses by "intrusion" or "internalisation," i.

Watching films with magical content facilitates creativity in children. Two experiments examined the possible link between magical thinking and creativity in preschool children. In Exp. Results indicated that the mean scores of children shown the magical film was significantly higher than that of children watching the nonmagical film on the majority of subsequent creativity tests for both age groups.

This trend was also found for 6-yr. Exposing children to a film with a magical theme did not affect their beliefs about magic. The results were interpreted to accentuate the role of magical thinking in children's cognitive development. Classroom implications of the results were also discussed.

Magical thinking by inpatient staff members. Magical thinking is a primitive form of mental activity which, nevertheless, the author contends, is common among mental health professionals. Four examples of magical thinking by inpatient staff members are presented and briefly explored, in order to shed light on our work and ourselves.

Anaerobic threshold, is it a magic number to determine fitness for surgery? The use of cardiopulmonary exercise testing CPET to evaluate cardiac and respiratory function was pioneered as part of preoperative assessment in the mid s. Surgical procedures have changed since then.

The patient population may have aged; however, the physiology has remained the same. The use of an accurate physiological evaluation remains as germane today as it was then. Certainly no ' magic ' is involved. The author recognizes that not everyone accepts the classical theories of the anaerobic threshold AT and that there is some discussion around lactate and exercise.

The article looks at aerobic capacity as an important predictor of perioperative mortality and also looks at some aspects of CPET relative to surgical risk evaluation. Secrets of the Chinese magic mirror replica. We examine the structure of five Chinese magic mirror replicas using a special imaging technique developed by the authors. All mirrors are found to have a two-layered structure.

The reflecting surface that gives rise to a projected magic pattern on the screen is hidden under a polished half-reflecting top layer. An alternative method of making the magic mirror using ancient technology has been proposed. Finally, we suggest a simple method of reconstructing a mirror replica in the laboratory.

Magic and the aesthetic illusion. The aesthetic illusion is the subjective experience that the content of a work of art is reality. It has an intrinsic relation to magic , an intrapsychic maneuver oriented toward modification and control of the extraspyschic world, principally through ego functioning. Magic is ontogenetically and culturally archaic, expresses the omnipotence inherent in primary narcissism, and operates according to the logic of the primary process. Magic is a constituent of all ego functioning, usually latent in later development.

It may persist as an archaic feature or may be evoked regressively in global or circumscribed ways. It causes a general disinhibition of instincts and impulses attended by a sense of confidence, exhiliration, and exuberance. The aesthetic illusion is a combination of illusions: 1 that the daydream embodied by the work of art is the beholder's own, the artist being ignored, and 2 that the artistically described protagonist is a real person with a real "world.

Both illusions are instances of magic. Accordingly, the aesthetic illusion is accompanied by a heady experience of excitement and euphoria. The relation among the aesthetic illusion, magic , and enthusiasm is illustrated by an analytic case, J.

We investigate a possible new doubly magic heavy nucleus by using a relativistic mean-field RMF model with the addition of a cross interaction term of omega-rho mesons and an electromagnetic exchange term.

Weiner May L io Weiner May THE In the postmodern countries the computer generated virtual reality provides new perceptual domains wherein the evaluation of real and unreal contents generates an essential challenge for both children and adults. The expectances to perceive unreal content which is contradictory with the common sense experiences become seductive for most of people. The time in front of the screen that emits the magic reality gradually rises.

The sudden advance in generation of alternative realities demands that we have to recall the basic principles of psychological reality testing and the involving mechanism that produces a distinction between phantasy and reality for both healthy and pathological mind. Frame of reference usually restrains the thinking. This review contains two parts, the first is focuses on the historical aspect of magical and physical reality and the second one, that will be published in a next issue, will present an evaluation of the boundary between self and another person in point of view of the psychopathological phenomenon.

This analysis will focus on how the boundary of the self behaves in physically real and magic computer generated environment. Working wonders? We propose a new approach to differentiate between insight and noninsight problem solving, by introducing magic tricks as problem solving domain.

We argue that magic tricks are ideally suited to investigate representational change, the key mechanism that yields sudden insight into the solution of a problem, because in order to gain insight into the magicians' secret method, observers must overcome implicit constraints and thus change their problem representation. In Experiment 1, 50 participants were exposed to 34 different magic tricks, asking them to find out how the trick was accomplished. Upon solving a trick, participants indicated if they had reached the solution either with or without insight.

Insight was reported in The new task domain revealed differences in solution accuracy, time course and solution confidence with insight solutions being more likely to be true, reached earlier, and obtaining higher confidence ratings. In Experiment 2, we explored which role self-imposed constraints actually play in magic tricks.

One group received verbal cues, providing solution relevant information without giving the solution away. The control group received no informative cue. Experiment 2 showed that participants' constraints were suggestible to verbal cues, resulting in higher solution rates. Thus, magic tricks provide more detailed information about the differences between insightful and noninsightful problem solving, and the underlying mechanisms that are necessary to have an insight.

All rights reserved. Magic in the machine: a computational magician's assistant. A human magician blends science, psychology, and performance to create a magical effect. In this paper we explore what can be achieved when that human intelligence is replaced or assisted by machine intelligence. Magical effects are all in some form based on hidden mathematical, scientific, or psychological principles; often the parameters controlling these underpinning techniques are hard for a magician to blend to maximize the magical effect required.

The complexity is often caused by interacting and often conflicting physical and psychological constraints that need to be optimally balanced.

Normally this tuning is done by trial and error, combined with human intuitions. Here we focus on applying Artificial Intelligence methods to the creation and optimization of magic tricks exploiting mathematical principles. We use experimentally derived data about particular perceptual and cognitive features, combined with a model of the underlying mathematical process to provide a psychologically valid metric to allow optimization of magical impact.

In the paper we introduce our optimization methodology and describe how it can be flexibly applied to a range of different types of mathematics based tricks. We also provide two case studies as exemplars of the methodology at work: a magical jigsaw, and a mind reading card trick effect.

We evaluate each trick created through testing in laboratory and public performances, and further demonstrate the real world efficacy of our approach for professional performers through sales of the tricks in a reputable magic shop in London.

This design allows broadband power combining with high isolation between the H port and E port, and achieves a lower insertion loss than any other broadband planar magic -T. The in-phase signal combiner consists of two quarter-wavelength-long transmission lines combined at the microstrip line junction. The out-of-phase signal combiner consists of two half-wavelength-long transmission lines combined in series. Structural symmetry creates a virtual ground plane at the combining junction, and the combined signal is converted from microstrip line to slotline.

Optimum realizable characteristic impedances are used so that the magic -T provides broadband response with low return loss. The magic -T is used in microwave and millimeter-wave frequencies, with the operating bandwidth being approximately percent. The minimum isolation obtainable is 32 dB from port E to port H. Operating temperature is mainly dependent on the variation in the dielectric constant of the substrate.

Using crystallized substrate, the invention can operate in an extremely broad range of temperatures from 0 to K. It has a very high reliability because it has no moving parts and requires no maintenance, though it is desirable that the magic -T operate in a low-humidity environment.

Fabrication of this design is very simple, using only two metallized layers. No bond wires, via holes, or air bridges are required. Additionally, this magic -T can operate as an individual component without auxiliary components.

Background and aims: Lecturers often present entertaining videos, or organize a variety of amusing demonstrations, to foster student engagement or to encourage critical analysis.

Magic tricks, in particular, have been shown to activate neural circuits that underpin motivation or problem-solving and, therefore, could be beneficial during lectures.

Generally speaking, a distance magic -type labeling of a graph G of order n is a bijection l from the vertex set of the graph to the first n natural numbers or to the elements of a group of order n, with the property that the weight of each vertex is the same.

The weight of a vertex x is defined as the sum or appropriate group operation of all the labels of vertices adjacent to x. If instead we require that all weights differ, then we refer to the labeling as a distance antimagic-type labeling. This idea can be generalized for directed graphs; the weight will take into consideration the direction of the arcs. In this manuscript, we provide new results for d-handicap labeling, a distance antimagic-type labeling, and introduce a new distance magic -type labeling called orientable Gamma-distance magic labeling.

If a graph G admits a d-handicap labeling, we say G is a d-handicap graph. That is, strength of schedule increases arithmetically with strength of team. Constructing an H n,k,d is equivalent to finding a d-handicap labeling of a k-regular graph of order n.. In Chapter 2 we provide general constructions for every d for large classes of both n and k, providing breadfth and depth to the catalog of known H n,k,d 's. In Chapters 3 - 6, we introduce a new type of labeling called orientable Gamma-distance magic labeling.

Let Gamma be an abelian group of order. Finding All Solutions to the Magic Hexagram.



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