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- Neutrosophic logic (3)
- Combinatorics (2)
- Graph theory (2)
- Infinite products (2)
- Reproducing kernels (2)
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- Slice hyperholomorphic functions (2)
- Abel Grassmann groupoid (1)
- Bernoulli measures (1)
- Blaschke-Potapov product (1)
- Bochner theorem (1)
- Boundary-representations (1)
- Combinatorial game theory (1)
- Covariance (1)
- Cuntz algebras (1)
- Cuntz-relations (1)
- Description (1)
- Direct integral decompositions (1)
- Domineering (1)
- Dynamical systems (1)
- Filter banks (1)
- Fuzzy mod planes (1)
- Fuzzy semigroup (1)
- Gaussian processes (1)
- Graph (1)
- Groupoid (1)
- Hackenbush (1)
- Hanoi variant (1)
- Herglotz integral representation theorem (1)
- Independence (1)
- Inner product spaces (1)
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- Mathematics, Physics, and Computer Science Faculty Articles and Research (11)
- Branch Mathematics and Statistics Faculty and Staff Publications (6)
- Electronic Theses and Dissertations (2)
- Applications and Applied Mathematics: An International Journal (AAM) (1)
- Idaho Conference on Undergraduate Research (1)
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Articles 1 - 21 of 21
Full-Text Articles in Other Mathematics
In Honor And Memory Of Professor Lajos Takács, Aliakbar M. Haghighi, Sri G. Mohanty
In Honor And Memory Of Professor Lajos Takács, Aliakbar M. Haghighi, Sri G. Mohanty
Applications and Applied Mathematics: An International Journal (AAM)
This issue of AAM is dedicated to honoring and remembering Professor Lajos Takács. While wrapping up the manuscript of my book (co-authored by Dr. Dimitar Mishev): Delayed and Network Queues, I went back to celebrate his 1962 book, Introduction to the Theory of Queues, where he gives an example illustrating a waiting time paradox, where the waiting time of a passenger waiting for a bus at a bus stop is infinite, while, in reality, he will wait a finite unit of time before a bus arrive. I sent Professor Takács an e-mail on December 4, 2015, inquiring if he had …
Generalizations And Algebraic Structures Of The Grøstl-Based Primitives, Dmitriy Khripkov, Nicholas Lacasse, Bai Lin, Michelle Mastrianni, Liljana Babinkostova (Mentor)
Generalizations And Algebraic Structures Of The Grøstl-Based Primitives, Dmitriy Khripkov, Nicholas Lacasse, Bai Lin, Michelle Mastrianni, Liljana Babinkostova (Mentor)
Idaho Conference on Undergraduate Research
With the large scale proliferation of networked devices ranging from medical implants like pacemakers and insulin pumps, to corporate information assets, secure authentication, data integrity and confidentiality have become some of the central goals for cybersecurity. Cryptographic hash functions have many applications in information security and are commonly used to verify data authenticity. Our research focuses on the study of the properties that dictate the security of a cryptographic hash functions that use Even-Mansour type of ciphers in their underlying structure. In particular, we investigate the algebraic design requirements of the Grøstl hash function and its generalizations. Grøstl is an …
The Apprentices' Tower Of Hanoi, Cory Bh Ball
The Apprentices' Tower Of Hanoi, Cory Bh Ball
Electronic Theses and Dissertations
The Apprentices' Tower of Hanoi is introduced in this thesis. Several bounds are found in regards to optimal algorithms which solve the puzzle. Graph theoretic properties of the associated state graphs are explored. A brief summary of other Tower of Hanoi variants is also presented.
Mod Planes: A New Dimension To Modulo Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Mod Planes: A New Dimension To Modulo Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book for the first time authors study mod planes using modulo intervals [0, m); 2 ≤ m ≤ ∞. These planes unlike the real plane have only one quadrant so the study is carried out in a compact space but infinite in dimension. We have given seven mod planes viz real mod planes (mod real plane) finite complex mod plane, neutrosophic mod plane, fuzzy mod plane, (or mod fuzzy plane), mod dual number plane, mod special dual like number plane and mod special quasi dual number plane. These mod planes unlike real plane or complex plane or neutrosophic …
On Algebras Which Are Inductive Limits Of Banach Spaces, Daniel Alpay, Guy Salomon
On Algebras Which Are Inductive Limits Of Banach Spaces, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce algebras which are inductive limits of Banach spaces and carry inequalities which are counterparts of the inequality for the norm in a Banach algebra. We then define an associated Wiener algebra, and prove the corresponding version of the well-known Wiener theorem. Finally, we consider factorization theory in these algebra, and in particular, in the associated Wiener algebra.
Boundary Interpolation For Slice Hyperholomorphic Schur Functions, Khaled Abu-Ghanem, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini
Boundary Interpolation For Slice Hyperholomorphic Schur Functions, Khaled Abu-Ghanem, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers κ1,…,κN, quaternions p1,…,pN all of modulus 1, so that the 2-spheres determined by each point do not intersect and pu≠1 for u=1,…,N, and quaternions s1,…,sN, we wish to find a slice hyperholomorphic Schur function s so that
limr→1r∈(0,1)s(rpu)=suforu=1,…,N,
and
limr→1r∈(0,1)1−s(rpu)su¯¯¯¯¯1−r≤κu,foru=1,…,N.
Our arguments relies on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces.
Spectral Theory For Gaussian Processes: Reproducing Kernels, Random Functions, Boundaries, And L2-Wavelet Generators With Fractional Scales, Daniel Alpay
Mathematics, Physics, and Computer Science Faculty Articles and Research
A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by a host of applications, e.g., in mathematical physics, and in stochastic differential equations, and their use in financial models. In this paper, we show that, for three classes of cases in the correspondence, it is possible to obtain explicit formulas which are amenable to computations of the respective Gaussian stochastic processes. For achieving this, we first develop two functional analytic tools. They are: …
Neutrosophic Graphs: A New Dimension To Graph Theory, Florentin Smarandache, Wb. Vasantha Kandasamy, K. Ilanthenral
Neutrosophic Graphs: A New Dimension To Graph Theory, Florentin Smarandache, Wb. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time have made a through study of neutrosophic graphs. This study reveals that these neutrosophic graphs give a new dimension to graph theory. The important feature of this book is it contains over 200 neutrosophic graphs to provide better understanding of this concepts. Further these graphs happen to behave in a unique way inmost cases, for even the edge colouring problem is different from the classical one. Several directions and dimensions in graph theory are obtained from this study. Finally certainly these new notions of neutrosophic graphs in general and in particular the …
Special Type Of Topological Spaces Using [0, N), Florentin Smarandache, W.B Vasantha Kandasamy
Special Type Of Topological Spaces Using [0, N), Florentin Smarandache, W.B Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time introduce the notion of special type of topological spaces using the interval [0, n). They are very different from the usual topological spaces. Algebraic structure using the interval [0, n) have been systemically dealt by the authors. Now using those algebraic structures in this book authors introduce the notion of special type of topological spaces. Using the super subset interval semigroup special type of super interval topological spaces are built. Several interesting results in this direction are obtained. Next six types of topological spaces using subset interval pseudo ring semiring of type …
Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the notion of MOD functions are defined on MOD planes. This new concept of MOD functions behaves in a very different way. Even very simple functions like y = nx has several zeros in MOD planes where as they are nice single line graphs with only (0, 0) as the only zero. Further polynomials in MOD planes do not in general follows the usual or classical laws of differentiation or integration. Even finding roots of MOD polynomials happens to be very difficult as they do not follow the fundamental theorem of algebra, viz a nth degree polynomial …
Self-Mappings Of The Quaternionic Unit Ball: Multiplier Properties, Schwarz-Pick Inequality, And Nevanlinna-Pick Interpolation Problem, Daniel Alpay, Vladimir Bolotnikov, Fabrizio Colombo, Irene Sabadini, Fabrizio Colombo
Self-Mappings Of The Quaternionic Unit Ball: Multiplier Properties, Schwarz-Pick Inequality, And Nevanlinna-Pick Interpolation Problem, Daniel Alpay, Vladimir Bolotnikov, Fabrizio Colombo, Irene Sabadini, Fabrizio Colombo
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study several aspects concerning slice regular functions mapping the quaternionic open unit ball B into itself. We characterize these functions in terms of their Taylor coefficients at the origin and identify them as contractive multipliers of the Hardy space H2(B). In addition, we formulate and solve the Nevanlinna-Pick interpolation problem in the class of such functions presenting necessary and sufficient conditions for the existence and for the uniqueness of a solution. Finally, we describe all solutions to the problem in the indeterminate case.
Realizations Of Infinite Products, Ruelle Operators And Wavelet Filters, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
Realizations Of Infinite Products, Ruelle Operators And Wavelet Filters, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using the system theory notion of state-space realization of matrix-valued rational functions, we describe the Ruelle operator associated with wavelet filters. The resulting realization of infinite products of rational functions have the following four features: 1) It is defined in an infinite-dimensional complex domain. 2) Starting with a realization of a single rational matrix-function M, we show that a resulting infinite product realization obtained from M takes the form of an (infinitedimensional) Toeplitz operator with the symbol that is a reflection of the initial realization for M. 3) Starting with a subclass of rational matrix functions, including scalar-valued ones corresponding …
Wiener-Chaos Approach To Optimal Prediction, Daniel Alpay, Alon Kipnis
Wiener-Chaos Approach To Optimal Prediction, Daniel Alpay, Alon Kipnis
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this work we combine Wiener chaos expansion approach to study the dynamics of a stochastic system with the classical problem of the prediction of a Gaussian process based on part of its sample path. This is done by considering special bases for the Gaussian space G generated by the process, which allows us to obtain an orthogonal basis for the Fock space of G such that each basis element is either measurable or independent with respect to the given samples. This allows us to easily derive the chaos expansion of a random variable conditioned on part of the sample …
Quaternionic Hardy Spaces In The Open Unit Ball And Half Space And Blaschke Products, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Quaternionic Hardy Spaces In The Open Unit Ball And Half Space And Blaschke Products, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
The Hardy spaces H2(B) and H2(H+), where B and H+ denote, respectively, the open unit ball of the quaternions and the half space of quaternions with positive real part, as well as Blaschke products, have been intensively studied in a series of papers where they are used as a tool to prove other results in Schur analysis. This paper gives an overview on the topic, collecting the various results available.
An Extension Of Herglotz's Theorem To The Quaternions, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini, David P. Kimsey
An Extension Of Herglotz's Theorem To The Quaternions, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini, David P. Kimsey
Mathematics, Physics, and Computer Science Faculty Articles and Research
A classical theorem of Herglotz states that a function n↦r(n) from Z into Cs×s is positive definite if and only there exists a Cs×s-valued positive measure dμ on [0,2π] such that r(n)=∫2π0eintdμ(t)for n∈Z. We prove a quaternionic analogue of this result when the function is allowed to have a number of negative squares. A key tool in the argument is the theory of slice hyperholomorphic functions, and the representation of such functions which have a positive real part in the unit ball of the quaternions. We study in great detail the case of positive definite functions.
A New Resolvent Equation For The S-Functional Calculus, Daniel Alpay, Fabrizio Colombo, Jonathan Gantner, Irene Sabadini
A New Resolvent Equation For The S-Functional Calculus, Daniel Alpay, Fabrizio Colombo, Jonathan Gantner, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
The S-functional calculus is a functional calculus for (n + 1)-tuples of non necessarily commuting operators that can be considered a higher dimensional version of the classical Riesz-Dunford functional calculus for a single operator. In this last calculus, the resolvent equation plays an important role in the proof of several results. Associated with the S-functional calculus there are two resolvent operators: the left S−1 L (s, T ) and the right one S−1 R (s, T ), where s = (s0, s1, . . . , sn) ∈ Rn+1 and T = (T0, T1, . . . , Tn) is …
Infinite Product Representations For Kernels And Iteration Of Functions, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Itzik Marziano
Infinite Product Representations For Kernels And Iteration Of Functions, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Itzik Marziano
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study infinite products of reproducing kernels with view to their use in dynamics (of iterated function systems), in harmonic analysis, and in stochastic processes. On the way, we construct a new family of representations of the Cuntz relations. Then, using these representations we associate a fixed filled Julia set with a Hilbert space. This is based on analysis and conformal geometry of a fixed rational mapping R in one complex variable, and its iterations.
Inner Product Spaces And Krein Spaces In The Quaternionic Setting, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Inner Product Spaces And Krein Spaces In The Quaternionic Setting, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we provide a study of quaternionic inner product spaces. This includes ortho-complemented subspaces, fundamental decompositions as well as a number of results of topological nature. Our main purpose is to show that a closed uniformly positive subspace in a quaternionic Krein space is ortho-complemented, and this leads to our choice of the results presented in the paper.
Mod Pseudo Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Mod Pseudo Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time elaborately study the notion of MOD vector spaces and MOD pseudo linear algebras. This study is new, innovative and leaves several open conjectures. In the first place as distributive law is not true we can define only MOD pseudo linear algebras. Secondly most of the classical theorems true in case of linear algebras are not true in case of MOD pseudo linear algebras. Finding even eigen values and eigen vectors happens to be a challenging problem. Further the notion of multidimensional MOD pseudo linear algebras are defined using the notion of MOD …
Fuzzy Abel Grassmann Groupoids, Florentin Smarandache, Madad Khan, Tariq Aziz
Fuzzy Abel Grassmann Groupoids, Florentin Smarandache, Madad Khan, Tariq Aziz
Branch Mathematics and Statistics Faculty and Staff Publications
Usually the models of real world problems in almost all disciplines like engineering, medical sciences, mathematics, physics, computer science, management sciences, operations research and articial intelligence are mostly full of complexities and consist of several types of uncertainties while dealing them in several occasion. To overcome these di¢ culties of uncertainties, many theories have been developed such as rough sets theory, probability theory, fuzzy sets theory, theory of vague sets, theory of soft ideals and the theory of intuitionistic fuzzy sets, theory of neutrosophic sets, Dezert-Smarandache Theory (DSmT), etc. Zadeh introduced the degree of membership/truth (t) in 1965 and dened …
Combinatorial Game Theory: An Introduction To Tree Topplers, John S. Ryals Jr.
Combinatorial Game Theory: An Introduction To Tree Topplers, John S. Ryals Jr.
Electronic Theses and Dissertations
The purpose of this thesis is to introduce a new game, Tree Topplers, into the field of Combinatorial Game Theory. Before covering the actual material, a brief background of Combinatorial Game Theory is presented, including how to assign advantage values to combinatorial games, as well as information on another, related game known as Domineering. Please note that this document contains color images so please keep that in mind when printing.