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A Variable Structural Control for a Hybrid Hyperbolic Dynamic System
Full text linkAbstract: In this paper, we are concerned with a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a variable structural control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by the ideal variable structural mode under control in any accuracy is derived and examined
Six Reasons to Discard Wave Particle Duality: Thereby Opening New Territory for Young Scientists to Explore
Full text linkWave particle duality is a cornerstone of quantum chemistry and quantum mechanics (QM). But there are experiments it cannot explain, such as a neutron interferometer experiment. If QM uses Ψ as its wavefunction, several experiments suggest that nature uses -Ψ instead. The difference between -Ψ and +Ψ is that they describe entirely different pictures of how nature is organized. For example, with -Ψ quantum particles follow waves backwards, which is incompatible with wave-particle-duality, obviously. We call the -Ψ proposal the Theory of Elementary Waves (TEW). It unlocks opportunities for young scientists with no budget to conduct the basic research for a new, unexplored science. This is a dream come true for young scientists: the discovery of uncharted territory. We show how TEW explains the double slit, Pfleegor Mandel and Davisson Germer experiments, Feynman diagrams and the Bell test experiments. We provide innovative research designs for which -Ψ and +Ψ would predict divergent outcomes. What makes QM so accurate is its probability predictions. But Born’s law would yield the same probabilities if it were changed from P = |+Ψ |2 to P = |-Ψ |2. This article is accompanied by a lively YouTube video, “6 reasons to discard wave particle duality.
PDE boundary conditions that eliminate quantum weirdness: a mathematical game inspired by Kurt Gödel and Alan Turing
Full text linkAlthough boundary condition problems in quantum mathematics (QM) are well known, no one ever used boundary conditions technology to abolish quantum weirdness. We employ boundary conditions to build a mathematical game that is fun to learn, and by using it you will discover that quantum weirdness evaporates and vanishes. Our clever game is so designed that you can solve the boundary condition problems for a single point if-and-only-if you also solve the “weirdness” problem for all of quantum mathematics. Our approach differs radically from Dirichlet, Neumann, Robin, or Wolfram Alpha. We define domain Ω in one-dimension, on which a partial differential equation (PDE) is defined. Point α on ∂Ω is the location of a boundary condition game that involves an off-center bi-directional wave solution called Æ, an “elementary wave.” Study of this unusual, complex wave is called the Theory of Elementary Waves (TEW). We are inspired by Kurt Gödel and Alan Turing who built mathematical games that demonstrated that axiomatization of all mathematics was impossible. In our machine quantum weirdness vanishes if understood from the perspective of a single point α, because that pinpoint teaches us that nature is organized differently than we expect
On the existence of positive solutions for a nonlinear elliptic class of equations in R2 and R3
Full text linkWe study the existence of positive solutions for an elliptic equation in RN for N = 2, 3 which is related with the existence of standing (localized) waves and the existence of the ground state solutions for some physical model or systems in fluid mechanics to describe the evolution of weakly nonlinear water waves. We use a variational approach and the well-known principle of concentration-compactness due to P. Lions to obtain the existence of this type of solutions, even in the case that the nonlinear term g is a non-homogeneous function or an operator defined in H1(RN) with values in R
Second Order Partial Derivatives
Full text linkThe rules for calculating partial derivatives and differentials are the same as for calculating the derivative of a function of one variable, except that when finding partial derivatives per one variable, the other variables are considered as constant
Coefficient Estimates for Some Subclasses of m-Fold Symmetric Bi-univalent Functions Defined by Linear Operator
Full text link The articles introduces and investigates "two new subclasses of the bi-univalent functions ." These are analytical functions related to the m-fold symmetric function and . We calculate the initial coefficients for all the functions that belong to them, as well as the coefficients for the functions that belong to a field where finding these coefficients requires a complicated method. Between the remaining results, the upper bounds for "the initial coefficients "are found in our study as well as several examples. We also provide a general formula for the function and its inverse in the m-field. A function is called analytical if it does not take the same values twice . It is called a univalent function if it is analytical at all its points, and the function is called a bi-univalent if it and its inverse are univalent functions together. We also discuss other concepts and important terms.
Expectation of Rice Pod Production in Iraq by Using Time Series
Full text linkThe research aims to shed light on the reality of the production of Rice pods in Iraq during the period of time (1943-2019) and its development with time, then predict the production of Rice pods based on three Models of prediction Models, which are the time regression Model on production, in addition to studying the effect of harvested area on production quantities. Then forecasting the production of the Rice pods according to the Model of the regression of the harvested area on the production, the Autoregression Model, and the integrative moving averages (Box Jenkins Models), and in the end the comparison between the expected values of production through the three Models to know the best Model to represent the time series of production of the Rice pods , through the use of the statistical program (SPSS (, Based on annual secondary data represented by the quantities of Rice pods, and the size of the harvested areas of this material in Iraq for the period from 1945 until 2019 obtained from (Central Statistical Organization, Iraq, 2020
Golden Ratio, Silver Ratio and other Metallic Means ; Geometric Substantiation of all Metallic Ratios
No full textThis paper introduces the concept of special right angled triangles those epitomize the different Metallic Ratios. These right triangles not only have the precise Metallic Means embedded in all their geometric features, but they also provide the most accurate geometric substantiation of all Metallic Means. These special right triangles manifest the corresponding Metallic Ratios more holistically than the regular pentagon, octagon or tridecagon, et
Metallic Ratios in Primitive Pythagorean Triples : Metallic Means embedded in Pythagorean Triangles and other Right Triangles
Full text linkThe Primitive Pythagorean Triples are found to be the purest expressions of various Metallic Ratios. Each Metallic Mean is epitomized by one particular Pythagorean Triangle. Also, the Right Angled Triangles are found to be more “Metallic” than the Pentagons, Octagons or any other (n2+4)gons. The Primitive Pythagorean Triples, not the regular polygons, are the prototypical forms of all Metallic Means
Squared prime numbers: Methods giving all prime numbers endless
Full text linkMy investigation shows that there is a regularity even by the prime numbers. This structure is obvious when a prime square is created. The squared prime numbers.
1. Connections in a prime square
A prime square (or origin square) is defined as a square consisting of as many boxes as the origin prim squared. This prime settle every side of the square. So, for example, the origin square 17 have got four sides with 17 boxes along every side. The prime numbers in each of the 289 boxes are filled with primes when a prime number occur in the number series (1,2,3,4,5,6,7,8,9 and so on) and then is noted in that very box.
If a box is occupied in the origin square A this prime number could be transferred to the corresponding box in a second square B, and thereafter the counting and noting continue in the first square A. Eventually we get two filled prime squares. Analyzing these squares, you leave out the right vertical line, representing only the origin prime number,
When a square is filled with primes you subdivide it into four corner squares, as big as possible, denoted a, b, c and d clockwise. You also get a center line between the left and right vertical sides.
Irrespective of what kind of constellation you activate this is what you find:
Every constellation in the corner square a and/or d added to a corresponding constellation in the corner square b and/or c is evenly divisible with the origin prime.
Every constellation in the corner square a and/or b added to a corresponding constellation in the corner square d and/or c is not evenly divisible with the origin prime.
Every reflecting constellation inside two of the opposed diagonal corner squares, possibly summarized with any optional reflecting constellation inside the two other diagonal corner squares, is evenly divisible with the origin prime squared. You may even add a reflection inside the center line and get this result.
My Conjecture 1 is that this applies to every prime square without end.
A formula giving all prime numbers endless
In the second prime square the prime numbers are always higher than in the first square if you compare a specific box. There is a mathematic connection between the prime numbers in the first and second square. This connection appears when you square and double the origin prime and thereafter add this number to the prime you investigate. A new higher prime is found after n additions.
You start with lowest applicable prime number 3 and its square 3². Double it and you get 18. We add 18 to the six next prime numbers 5, 7, 11, 13, 17 and 19 in any order. After a few adds you get a prime and after another few adds you get another higher one. In this way you continue as long as you want to. The primes are creating themselves.
A formula giving all prime numbers is:
5+18×n, +18×n, +18×n … without end
7+18×n, +18×n, +18×n … without end
11+18×n, +18×n, +18×n … without end
13+18×n, +18×n, +18×n … without end
17+18×n, +18×n, +18×n … without end
19+18×n, +18×n, +18×n … without end
The letter n in the formula stands for how many 18-adds you must do until the next prime is found.
My Conjecture 2 is that this you find every prime number by adding 18 to the primes 5, 7, 11, 13, 17 and 19 one by one endless.
A method giving all prime numbers endless
There is still a possibility to even more precise all prime numbers. You start a 5-number series derived from the start primes 7, 17, 19, 11, 13 and 5 in that very order. Factorized these number always begin with number 5. When each of these numbers are divided with five the quotient is either a prime number or a composite number containing of two or some more prime numbers in the nearby. By sorting out all the composite quotients you get all the prime numbers endless and in order.
Every composite quotient starts with a prime from 5 and up, squared. Thereafter the quotients starting with that prime show up periodically according to a pattern of short and long sequences. The position for each new prime beginning the composite quotient is this prime squared and multiplied with 5. Thereafter the short sequence is this prime multiplied with 10, while the long sequence is this prime multiplied with 20.
When all the composite quotients are deleted there are left several 5-numbers which divided with 5 give all prime numbers, and you even see clearly the distance between the prime numbers which for instance explain why the prime twins occur as they do.
My Conjecture 3 is that this is an exact method giving all prime numbers endless and in order