Mathematics Commons^™

Vertex Antimagic Total Labeling Pada Graphmulticycle, Dominikus Arif Budi Prasetyo Pythagors

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Pelabelan graf merupakan bagian dari graf yang berkembang saat ini. Jenis pelabelan pada graf bergantungpada domainnya, yakni pelabelan sisi ajaib, pelabelan titik ajaib, dan pelabelan total ajaib. Pelabelan totalajaib pada graf dibedakan lagi berdasarkan komponen graf yang dievaluasi, yakni pelabelan total sisi ajaibdan pelabelan total titik ajaib. Pada pelabelan ajaib, bobot dari komponen graf yang dievaluasi adalah sama,jika bobotnya tidak sama maka dinamakan pelabelan tak-ajaib (antimagic). Misalkan G adalah graf denganbanyak titik p dan sisi q. Suatu pemetaan bijektif dari komponen-komponen graf ke bilangan bulat positif {1,2, "¦, (p+q)} disebut called (a, d) vertex antimagic total labelling (pelabelan total titik …

Construction A Coring From Tensor Product Of Bialgebra, Nikken Prima Puspita, Siti Khabibah

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

In this Paper introduced a coring from tensor product of bialgebra. An algebra with compatible coalgebrastructure are known as bialgebra. For any bialgebra B we can obtained tensor product between B anditself. Defined a right and left B -action on the tensor product of bialgebra B such that we have tensorproduct of B and itself is a bimodule over B. In this note we expect that the tensor product B anditself becomes a B -coring with comultiplication and counit.Keywords : action, algebra, coalgebra, coring.

Penerapan Teori Graf Pada Analisis Jejaring Sosialdengan Menggunakan Microsoft Microsoft Node Xl, Nur Insani, Nur Hadi Waryanto

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Pentingnya posisi seseorang di dalam jaringan ataupun suatu organisasi tidak hanya ditentukanoleh seberapa banyak ia terhubung oleh banyak orang tetapi apakah seseorang menjadi jembatan dariorang-orang yang memiliki banyak jaringan. Jadi bukanlah faktor centraliti yang merupakan faktor utamaseseorang dianggap penting, tetapi information broker, yaitu seseorang yang bukan pusat dariketerhubungan banyak orang namun memiliki hubungan dengan orang-orang yang memiliki banyakpengikut, memegang peranan yang lebih penting. Analisa Jejaring Sosial (AJS) memberikan peranpenting dalam menggambarkan interaksi informal dimana ia menggambarkan keadaan interaksi manusiasebagai mana keadaan nyata. Salah satu bentuk jejaring sosial yang dapat dianalisa adalah kepengurusanDekanat FMIPA Universitas Negeri Yogyakarta (UNY) sampai dengan kepengurusan …

Computational Chemistry Capacity Building In An Underprivileged Context: Challenges, Outcomes And Perspectives, L Mammino

Tanzania Journal of Science

Computational chemistry is a fast developing branch of modern chemistry, focusing on the study of molecules to enable better understanding of the properties of substances. Its applications comprise a variety of fields, from drug design to the design of compounds with desired properties (e.g., catalysts with specific actions) and to ample overlaps with nanotechnology. However, despite its relevance, the presence of computational chemistry research in Sub-Saharan Africa is still scarce, practically absent in many institutions. Bridging the gap with the other continents requires the identification of capacity building options that may enable a rapid growth. The recent experience at the …

Public Expenditure, Environmental Pollution And Endogenous Economic Growth., Trishita Ray Barman Dr.

Doctoral Theses

Sources of Economic Growth and the Definition of Steady-State EquilibriumEconomic growth is defined as a continuous increase in national income taking place over a time horizon. According to the neoclassical theory of economic growth there are three sources of economic growth: (i) capital accumulation, (ii) growth of labour force and (iii) technological progress.The steady-state growth equilibrium is defined as a state where all major macro-economic variables grow at the same rate so that the ratios of these variables remain unchanged over time. For example, in the one sector aggregative model like that of Solow (1956), capital and labour grow at …

Measures Of Centrality Based On The Spectrum Of The Laplacian, Scott D. Pauls, Daniel Remondini

Dartmouth Scholarship

We introduce a family of new centralities, the k-spectral centralities. k-Spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection, k-spectral centralities have various interpretations in terms of spectrally determined information.

We explore this centrality in the context of several examples. While for sparse unweighted net- works 1-spectral centrality behaves similarly to other standard centralities, for dense weighted net- works they show different properties. In summary, the k-spectral centralities provide a novel and useful measurement of relevance (for single network elements as well as whole subnetworks) …

The Convergence Of Two Algorithms For Compressed Sensing Based Tomography, Xiezhang Li, Jiehua Zhu

Mathematical Sciences: Faculty Publications

The constrained total variation minimization has been developed successfully for image reconstruction in computed tomography. In this paper, the block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework. The convergence of the algorithms under a certain condition is derived. Examples are given to illustrate their convergence behavior and noise performance.

Completion Of Hankel Partial Contractions Of Extremal Type, Raúl E. Curto, Sang Hoon Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

We find concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size 4 × 4 in the extremal case. Along the way we introduce a new approach that allows us to solve, algorithmically, the contractive completion problem for 4 × 4 Hankel matrices. As an application, we obtain a concrete example of a partially contractive 4 × 4 Hankel matrix, which does not admit a contractive completion.

An Elastica Model Of The Buckling Of A Nanoscale Sheet Perpendicular To A Rigid Substrate, Shawn D. Ryan, Dmitry Golovaty, Patrick Wilber

Mathematics and Statistics Faculty Publications

We study a variation on the classical problem of the buckling of an elastica. The elastica models a nanoscale sheet that interacts with a rigid substrate by intermolecular forces. We formulate a buckling problem in which the sheet is perpendicular to the substrate and a load is applied to the edge of the sheet further from the substrate. Our study is motivated by problems in nanomechanics such as the bending of a graphene sheet interacting with a rigid substrate by van der Waals forces. After identifying a trivial branch, we combine computation and analysis to determine the stability and bifurcations …

Cost Effective Domination In Graphs, Tabitha Lynn Mccoy

Electronic Theses and Dissertations

A set S of vertices in a graph G = (V,E) is a dominating set if every vertex in V \ S is adjacent to at least one vertex in S. A vertex v in a dominating set S is said to be it cost effective if it is adjacent to at least as many vertices in V \ S as it is in S. A dominating set S is cost effective if every vertex in S is cost effective. The minimum cardinality of a cost effective dominating set of G is the cost …

Blow-Up Of Solutions To The Generalized Inviscid Proudman-Johnson Equation, Alejandro Sarria

LSU New Orleans Theses and Dissertations

The generalized inviscid Proudman-Johnson equation serves as a model for n-dimensional incompressible Euler flow, gas dynamics, high-frequency waves in shallow waters, and orientation of waves in a massive director field of a nematic liquid crystal. Furthermore, the equation also serves as a tool for studying the role that the natural fluid processes of convection and stretching play in the formation of spontaneous singularities, or of their absence.

In this work, we study blow-up, and blow-up properties, in solutions to the generalized, inviscid Proudman-Johnson equation endowed with periodic or Dirichlet boundary conditions. More particularly,regularity of solutions in an Lp setting will …

Parametrizing Finite Frames And Optimal Frame Completions, Miriam J. Poteet

Theses and Dissertations

Frames are used in many signal processing applications. We consider the problem of constructing every frame whose frame operator has a given spectrum and whose vectors have prescribed lengths. For a given spectrum and set of lengths, we know when such a frame exists by the Schur-Horn Theorem; it exists if and only if its spectrum majorizes its squared lengths. We provide a more constructive proof of Horn's original result. This proof is based on a new method for constructing any and all frames whose frame operator has a prescribed spectrum and whose vectors have prescribed lengths. Constructing all such …

A Centre-Stable Manifold For The Energy-Critical Wave Equation In R^3 In The Symmetric Setting, Marius Beceanu

Mathematics and Statistics Faculty Scholarship

Consider the focusing semilinear wave equation in R^3 with energy-critical nonlinearity \partial_t^2 \psi - \Delta \psi - \psi^5 = 0, \psi(0) = \psi_0, \partial_t \psi(0) = \psi_1. This equation admits stationary solutions of the form \phi(x, a) := (3a)^{1/4} (1+a|x|^2)^{-1/2}, called solitons, which solve the elliptic equation -\Delta \phi - \phi^5 = 0. Restricting ourselves to the space of symmetric solutions \psi for which \psi(x) = \psi(-x), we find a local centre-stable manifold, in a neighborhood of \phi(x, 1), for this wave equation in the weighted Sobolev space ^{-1} \dot H^1 \times< x>^{-1} L^2. Solutions with initial data on the …

Strichartz Estimates And Maximal Operators For The Wave Equation In R^3, Marius Beceanu, Michael Goldberg

Mathematics and Statistics Faculty Scholarship

We prove sharp Strichartz-type estimates in three dimensions, including some which hold in reverse spacetime norms, for the wave equation with potential. These results are also tied to maximal operator estimates studied by Rogers--Villaroya, of which we prove a sharper version. As a sample application, we use these results to prove the local well-posedness and the global well-posedness for small initial data of semilinear wave equations in R^3 with quintic or higher monomial nonlinearities.

A Pointwise Estimate For The Fourier Transform And The Number Of Maxima Of A Function, Ryan Berndt

Mathematics Faculty Scholarship

We show a pointwise estimate for the Fourier transform on the line involving the number of times the function changes monotonicity. The contrapositive of the theorem may be used to find a lower bound to the number of local maxima of a function. We also show two applications of the theorem. The first is the two weight problem for the Fourier transform, and the second is estimating the number of roots of the derivative of a function.

Oscillation Results For Fourth-Order Nonlinear Dynamic Equations, Chenghui Zhang, Tongxing Li, Ravi P. Agarwal, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

This work is concerned with the oscillation of a certain class of fourth-order nonlinear dynamic equations on time scales. a new oscillation result and an example are included. © 2012 Elsevier Ltd. All rights reserved.

Jensen's Functionals On Time Scales, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić

Mathematics and Statistics Faculty Research & Creative Works

We consider Jensen's functionals on time scales and discuss its properties and applications. Further, we define weighted generalized and power means on time scales. by applying the properties of Jensen's functionals on these means, we obtain several refinements and converses of Hölder's inequality on time scales. Copyright © 2012 Matloob Anwar et al.

Nabla Fractional Calculus And Its Application In Analyzing Tumor Growth Of Cancer, Fang Wu

Masters Theses & Specialist Projects

This thesis consists of six chapters. In the first chapter, we review some basic definitions and concepts of fractional calculus. Then we introduce fractional difference equations involving the Riemann-Liouville operator of real number order between zero and one. In the second chapter, we apply the Brouwer fixed point and Contraction Mapping Theorems to prove that there exists a solution for up to the first order nabla fractional difference equation with an initial condition. In chapter three, we define a lower and an upper solution for up to the first order nabla fractional difference equation with an initial condition. Under certain …

A Bijective Proof Of A Factorization Formula For Specialized Macdonald Polynomials, Nicholas A. Loehr, Elizabeth Niese

Mathematics Faculty Research

Let μ and ν = (ν 1, . . . , ν k ) be partitions such that μ is obtained from ν by adding m parts of sizer. Descouens and Morita proved algebraically that the modified Macdonald polynomials

H~μ(X;q,t)

satisfy the identity

H~μ=H~νH~(r^m)

when the parameter t is specialize to an mth root of unity. Descouens, Morita, and Numata proved this formula bijectively when r ≤ ν k and

r∈{1,2}.

This note gives a bijective proof of the formula for all r ≤ ν k .

A Representation For Positive Functionals Of A Brownian Motion And An Application, P Sundar, Ming Tao

Communications on Stochastic Analysis

No abstract provided.