Dimension one

This research is built upon the determination of the Eigenpairs of one and two dimensional positive differential operators with periodic boundary conditions. The Schrödinger equation was solved for positive operators in both one and two dimensions. Fourier series were used to express the derivatives as the summation of Fourier terms. This led to a novel approach for the calculation of the eigenmodels of a perturbed potential well. The perturbation can be done via an electric field applied to the potential well.

88p runthenight07 01-03-2023 5 2   Download

In this study, two models were proposed: a five-stage SISP maturity model for defining SISP maturity and another one for assessing the degree of SISP maturity. The five SISP maturity levels were defined as: Rudimentary Planning, Ineffectual Planning, Attainable Planning, Sustainable Planning, and Adaptable Planning. The assessment model was structured as a third-order system, where eight first-order dimensions were termed as Form and Content, Collaboration, Policies, Stakeholders' Designation, Knowledge Bank, Technology, Time Dimension, and Viability.

472p runthenight04 02-02-2023 9 3   Download

The aim of this study is to develop a perspective on culture which would integrate the views of both opposing camps. By applying the principles of ancient Chinese philosophy, especially the Yin-Yang principle, a balanced, holistic conceptualization was proposed which hold that culture is composed of both a stable and a changing dimension, which dialectically transform into each other to give culture a certain degree of stability and inheritability on the one hand, and a momentum for change and variability on the other, in an ongoing, spiraling process of cultural emergence.

295p runthenight04 02-02-2023 6 4   Download

Bài giảng Vật lý 1 cung cấp cho người học những kiến thức như: Introduction to Physics; Motion in one dimension; Montion in two dimensions; The laws of motion; Work&Energy of the system; Linear Momentum and Motion of System; Rotation of rigid object about a fiexd axis. Angular momentum;...

183p banhnhut2003 18-03-2022 25 3   Download

The calculation of particular cases of two levels and uniform distributions of site and transition energies shows the applicability of the constructed expressions not only for site disorder system, but also for mixed system with both site and transition disorders. The blocking effect is studied and also discussed.

9p tamynhan8 04-11-2020 7 1   Download

Phase transition and the Casimir effect are studied in the complex scalar field with one spatial dimension to be compactified. It is shown that the phase transition is of the second order and the Casimir effect behaves quite differently depending on whether it’s under periodic or anti-periodic boundary conditions.

9p tamynhan8 04-11-2020 11 2   Download

This paper is about a class of strange attractors that have the dual property of occurring naturally and being amenable to analysis. Roughly speaking, a rank one attractor is an attractor that has some instability in one direction and strong contraction in m−1 directions, m here being the dimension of the phase space. The results of this paper can be summarized as follows. Among all maps with rank one attractors, we identify, inductively, subsets Gn, n = 1, 2, 3, · · · ,

133p dontetvui 17-01-2013 46 6   Download

Annals of Mathematics In this paper we will solve one of the central problems in dynamical systems: Theorem 1 (Density of hyperbolicity for real polynomials). Any real polynomial can be approximated by hyperbolic real polynomials of the same degree. Here we say that a real polynomial is hyperbolic or Axiom A, if the real line is the union of a repelling hyperbolic set, the basin of hyperbolic attracting periodic points and the basin of infinity.

39p noel_noel 17-01-2013 49 5   Download

D. Mumford conjectured in [33] that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra generated by certain classes κi of dimension 2i. For the purpose of calculating rational cohomology, one may replace the stable moduli space of Riemann surfaces by BΓ∞ , where Γ∞ is the group of isotopy classes of automorphisms of a smooth oriented connected surface of “large” genus. Tillmann’s theorem [44] that the plus construction makes BΓ∞ into an infinite loop space led to a stable homotopy version of Mumford’s conjecture, stronger than the original [24]. .

100p noel_noel 17-01-2013 37 6   Download

There are very few examples of Riemannian manifolds with positive sectional curvature known. In fact in dimensions above 24 all known examples are diffeomorphic to locally rank one symmetric spaces. We give a partial explanation of this phenomenon by showing that a positively curved, simply connected, compact manifold (M, g) is up to homotopy given by a rank one symmetric space, provided that its isometry group Iso(M, g) is large. More precisely we prove first that if dim(Iso(M, g)) ≥ 2 dim(M ) − 6, then M is tangentially homotopically equivalent to a rank one symmetric space or M...

63p noel_noel 17-01-2013 55 5   Download

SLEκ is a random growth process based on Loewner’s equation with driving parameter a one-dimensional Brownian motion running with speed κ. This process is intimately connected with scaling limits of percolation clusters and with the outer boundary of Brownian motion, and is conjectured to correspond to scaling limits of several other discrete processes in two dimensions. The present paper attempts a first systematic study of SLE. It is proved that for all κ = 8 the SLE trace is a path; for κ ∈ [0, 4] it is a simple path; for κ ∈ (4, 8) it is...

43p noel_noel 17-01-2013 46 7   Download

Reduction of the singularities of codimension one singular foliations in dimension three By Felipe Cano Contents 0. Introduction 1. Blowing-up singular foliations 1.1. Adapted singular foliations 1.2. Permissible centers 1.3. Vertical invariants 1.4. First properties of presimple singularities 2. Global strategy 2.1. Reduction to presimple singularities. Statement 2.2. Good points. Bad points. Equi-reduction 2.3. Finiteness of bad points 2.4. The influency locus 2.5. The local control theorem 2.6. Destroying cycles 2.7. Global criteria of blowing-up 3. Local control 3.1.

106p tuanloccuoi 04-01-2013 57 7   Download

An extension of the Littlewood Restriction Rule is given that covers all pertinent parameters and simplifies to the original under Littlewood’s hypotheses. Two formulas are derived for the Gelfand-Kirillov dimension of any unitary highest weight representation occurring in a dual pair setting, one in terms of the dual pair index and the other in terms of the highest weight.

40p tuanloccuoi 04-01-2013 45 6   Download

We construct a proper C 2 -smooth function on R4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C 2 -smooth counterexample to the Hamiltonian Seifert conjecture in dimension four. 1. Introduction The “Hamiltonian Seifert conjecture” is the question whether or not there exists a proper function on R2n whose Hamiltonian flow has no periodic orbits on at least one regular level set.

25p tuanloccuoi 04-01-2013 58 7   Download

We have attempted to improve and update this text while retaining the features that make it unique, namely, an emphasis on physical understanding, and the ability to estimate, evaluate, and predict results without blind reliance on computers, while still maintaining rigorous connection to the mathematical basis for quantum chemistry. We have inserted intomost chapters examples that allowimportant points to be emphasized, clarified, or extended. This has enabled us to keep intact most of the conceptual development familiar to past users.

726p banhkem0908 24-11-2012 91 7   Download

An array is a data structure that contains a number of variables which are accessed through computed indices. The variables contained in an array, also called the elements of the array, are all of the same type, and this type is called the element type of the array. An array has a rank which determines the number of indices associated with each array element. The rank of an array is also referred to as the dimensions of the array. An array with a rank of one is called a single-dimensional array, and an array with a rank greater than one...

26p tengteng16 27-12-2011 58 3   Download

For n  2, let PG(n, 2) be the finite projective geometry of dimension n over F2, the field of order 2. The elements or points of PG(n, 2) are the one-dimensional vector subspaces of Fn+1 2 ; the lines of PG(n, 2) are the two-dimensional vector subspaces of Fn+1 2 . Each such one-dimensional subspace {0, x} is represented by the non-zero vector x contained in it. For ease of notation, if {e0, e1, . . . , en} is a basis of Fn+1 2 and x is an element of PG(n, 2), then we denote x by a1 . . .as, where x = ea1 +·...

7p thulanh5 12-09-2011 34 2   Download

Tuyển tập các báo cáo nghiên cứu khoa học hay nhất của tạp chí toán học quốc tế đề tài: Monotonic subsequences in dimensions higher than one...

9p thulanh4 11-09-2011 44 1   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Một điều trị hoàn toàn của tán xạ năng lượng thấp trong một chiều...

30p matuot_266 27-08-2011 68 4   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Điểm trên các tương tác trong một chiều...

26p matuot_266 27-08-2011 53 3   Download