Analysis Commons^™

Solutions To The LP Mixed Boundary Value Problem In C1,1 Domains, Laura D. Croyle

Theses and Dissertations--Mathematics

We look at the mixed boundary value problem for elliptic operators in a bounded C^1,1(ℝⁿ) domain. The boundary is decomposed into disjoint parts, D and N, with Dirichlet and Neumann data, respectively. Expanding on work done by Ott and Brown, we find a larger range of values of p, 1 < p < n/(n-1), for which the L^p mixed problem has a unique solution with the non-tangential maximal function of the gradient in L^p(∂Ω).

Remling's Theorem On Canonical Systems, Keshav R. Acharya

Publications

In this paper, we extend the Remling’s Theorem on canonical systems that the ω limit points of the Hamiltonian under the shift map are reflectionless on the support of the absolutely continuous part of the spectral measure of a canonical system.

Nidus Idearum. Scilogs, Ii: De Rerum Consectatione, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Welcome into my scientific lab! My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings "ground", "opinion", "expectation"), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). In this second book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, some of them already put at work, others …

Computing Closed Forms For The Convergent Series $\Displaystyle\Sum_{N \In \Mathbb{Z}}\Frac{1}{(N^3+Bn^2+Cn+D)^K}$, Gagandeep K. Virk

Theses and Dissertations (Comprehensive)

In this thesis we discuss the various approaches that will be taken to evaluate and find a finite closed form for the sum $$\sum_{n \in \mathbb{Z}} \frac{1}{(n^3+Bn^2+Cn+D)^k}$$ where $B, C, D \in \mathbb{C}$ and $k$ is a positive integer. We begin this thesis by studying the cubic equations and discussing briefly various methods of finding their roots. Cardano's method (1545) for finding the roots of cubic polynomials is explored in detail as this method is used in later parts of the thesis to make calculations while evaluating the sums. Various tools and techniques from Fourier analysis are reviewed for these …

The Bourgain Spaces And Recovery Of Magnetic And Electric Potentials Of Schrödinger Operators, Yaowei Zhang

Theses and Dissertations--Mathematics

We consider the inverse problem for the magnetic Schrödinger operator with the assumption that the magnetic potential is in C^λ and the electric potential is of the form p₁ + div p₂ with p₁, p₂ ∈ C^λ. We use semiclassical pseudodifferential operators on semiclassical Sobolev spaces and Bourgain type spaces. The Bourgain type spaces are defined using the symbol of the operator h²Δ + hμ ⋅ D. Our main result gives a procedure for recovering the curl of the magnetic field and the electric potential from the Dirichlet to Neumann …

The Von Neumann Inequality For 3 × 3 Matrices, Greg Knese

Mathematics Faculty Research

This note details how recent work of Kosiński on the three point Pick interpolation problem on the polydisc can be used to prove the von Neumann inequality for d-tuples of commuting 3 x 3 contractive matrices.

Special Type Of Fixed Points Of Mod Matrix Operators, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce a special type of fixed points using MOD square matrix operators. These special type of fixed points are different from the usual classical fixed points. A study of this is carried out in this book. Several interesting properties are developed in this regard. The notion of these fixed points find many applications in the mathematical models which are dealt systematically by the authors in the forth coming books. These special type of fixed points or special realized limit cycles are always guaranteed as we use only MOD matrices as operators with …

Problems On Mod Structures, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time give several types of problems on MOD structures happens to be an interesting field of study as it makes the whole 4 quadrant plane into a single quadrant plane and the infinite line into a half closed open interval. So study in this direction will certainly yield several interesting results. The law of distributivity is not true. Further the MOD function in general do not obey all the laws of integration or differentiation. Likewise MOD polynomials in general do not satisfy the basic properties of polynomials like its roots etc. Thus over …

Mod Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Zadeh introduced the degree of membership/truth (t) in 1965 and defined the fuzzy set. Atanassov introduced the degree of nonmembership/ falsehood (f) in 1986 and defined the intuitionistic fuzzy set. Smarandache introduced the degree of indeterminacy/ neutrality (i) as independent component in 1995 (published in 1998) and defined the neutrosophic set on three components (t, i, f) = (truth, indeterminacy, falsehood): http://fs.gallup.unm.edu/FlorentinSmarandache.htm Etymology. The words “neutrosophy” and “neutrosophic” were coined/ invented by F. Smarandache in his 1998 book. Neutrosophy: A branch of philosophy, introduced by F. Smarandache in 1980, which studies the origin, nature, and scope of neutralities, as well …

Nidus Idearum. Scilogs, I: De Neutrosophia, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Welcome into my scientific lab! My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings "ground", "opinion", "expectation"), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). In this first books of scilogs collected from my nest of ideas, one may find new and old questions and solutions, some of them already put at work, others …

Mathematics For Everything With Combinatorics On Nature – A Report On The Promoter Dr. Linfan Mao Of Mathematical Combinatorics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The science’s function is realizing the natural world, developing our society in coordination with natural laws and the mathematics provides the quantitative tool and method for solving problems helping with that understanding. Generally, understanding a natural thing by mathematical ways or means to other sciences are respectively establishing mathematical model on typical characters of it with analysis first, and then forecasting its behaviors, and finally, directing human beings for hold on its essence by that model.

Semigroups On Mod Natural Neutrosophic Elements, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the notion of semigroups under + is constructed using the Mod natural neutrosophic integers or MOD natural neutrosophic-neutrosophic numbers or mod natural neutrosophic finite complex modulo integer or MOD natural neutrosophic dual number integers or MOD natural neutrosophic special dual like number or MOD natural neutrosophic special quasi dual numbers are analysed in a systematic way. All these semigroups under + have an idempotent subsemigroup under +. This is the first time we are able to give a class of idempotent subsemigroups under + by taking only those MOD natural neutrosophic elements

Mod Relational Maps Models And Mod Natural Neutrosophic Relational Maps Models, Florentin Smarandache, K. Ilanthenral, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Zadeh introduced the degree of membership/truth (t) in 1965 and defined the fuzzy set. Atanassov introduced the degree of non membership/falsehood (f) in 1986 and defined the intuitionistic fuzzy set. Smarandache introduced the degree of indeterminacy/neutrality (i) as independent component in 1995 (published in 1998) and defined the neutrosophic set on three components (t,i,f) = (truth, indeterminacy, falsehood). The words “neutrosophy” and “neutrosophic” were coined/invented by F. Smarandache in his 1998 book. Etymologically, “neutro-sophy” (noun) [French neutre 1), or complete information (sum of components = 1).

Mod Natural Neutrosophic Subset Topological Spaces And Kakutani’S Theorem, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time develop the notion of MOD natural neutrosophic subset special type of topological spaces using MOD natural neutrosophic dual numbers or MOD natural neutrosophic finite complex number or MOD natural neutrosophic-neutrosophic numbers and so on to build their respective MOD semigroups. Later they extend this concept to MOD interval subset semigroups and MOD interval neutrosophic subset semigroups. Using these MOD interval semigroups and MOD interval natural neutrosophic subset semigroups special type of subset topological spaces are built. Further using these MOD subsets we build MOD interval subset matrix semigroups and MOD interval subset …

Mod Natural Neutrosophic Subset Semigroups, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of MOD subsets using Zn ... On these MOD subsets the operation ‘+’ is defined, S(Zn) denotes the MOD subset and {S(Zn), +} happens to be only a Smarandache semigroup.

These S-semigroups enjoy several interesting properties. The notion of MOD universal subset and MOD absorbing subsets are defined and developed. {S(Zn), x } is also a semigroup and several properties associated with them are derived. MOD natural neutrosophic subsets forms only a semigroup under ‘+’. In fact the main feature enjoyed by this structure is they have subset idempotents …

Mod Cognitive Maps Models And Mod Natural Neutrosophic Cognitive Maps Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Zadeh introduced the degree of membership/truth (t) in 1965 and defined the fuzzy set. Atanassov introduced the degree of non membership/falsehood (f) in 1986 and defined the intuitionistic fuzzy set. Smarandache introduced the degree of indeterminacy/neutrality (i) as independent component in 1995 (published in 1998) and defined the neutrosophic set on three components (t,i,f) = (truth, indeterminacy, falsehood). The words “neutrosophy” and “neutrosophic” were coined/invented by F. Smarandache in his 1998 book. Etymologically, “neutro-sophy” (noun) [French neutre 1), or complete information (sum of components = 1).

Special Type Of Fixed Point Pairs Using Mod Rectangular Matrix Operators, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time define a special type of fixed points using MOD rectangular matrices as operators. In this case the special fixed points or limit cycles are pairs which is arrived after a finite number of iterations. Such study is both new and innovative for it can find lots of applications in mathematical modeling. Since all these Zn or I nZ or 〈Zn ∪ g〉 or 〈Zn ∪ g〉I or C(Zn) or CI(Zn) are all of finite order we are sure to arrive at a MOD fixed point pair or a MOD limit cycle pair …

Mathematics. Possible Subjects For The High School Entrance Examination And The Capacity Examination In Romania, Florentin Smarandache, Constantin Coanda, Ionuț Ivanescu

Branch Mathematics and Statistics Faculty and Staff Publications

The present book tries to offer students and teachers knowledge evaluation tools for all the chapters from the current Romanian mathematics syllabus. In the evolution of teenagers, the phase of admission in high schools mobilizes particular efforts and emotions. The present workbook aims to be a permanent advisor in the agitated period starting with the capacity examination and leading to the admittance to high school. The tests included in this workbook have a complementary character as opposed to the many materials written with the purpose to support all those who prepare for such examinations and they refer to the entire …

Sisteme Vibrante Trilobice, Florentin Smarandache, Mircea Eugen Selariu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

A Note On Vector Valued Discrete Schrödinger Operators, Keshav R. Acharya

Publications

The main purpose of this paper is to extend some theory of Schrödinger operators from one dimension to higher dimension. In particular, we will give systematic operator theoretic analysis for the Schrödinger equations in multidimensional space. To this end, we will provide the detail proves of some basic results that are necessary for further studies in these areas. In addition, we will introduce Titchmarsh- Weyl m− function of these equations and express m− function in term of the resolvent operators.