generating function
در نشریات گروه علوم پایه-
Given an integer $n\geq4$, how many inequivalent quadrilaterals with ordered integer sides and perimeter $n$ are there? Denoting such number by $Q(n)$, the answer is given by the following closed formula:\[Q(n)=\left\{ \dfrac{1}{576}n\left( n+3\right) \left( 2n+3\right) -\dfrac{\left( -1\right) ^{n}}{192}n\left( n-5\right) \right\} \cdot\]Keywords: Integer quadrilaterals, Ordered quadrilaterals, Integer partitions, generating function
-
In this study we define a new generalization of the hybrid Leonardo sequence consisting of the hybrid numbers with hybrid Leonardo numbers coefficients. We investigate some algebraic properties of this new sequence and also the generating function, exponential generating function, and the Binet formula related to this type of sequence. In addition, some identities are provided, such as Catalans and Cassini’s identities, and sums are related.
Keywords: Leonardo Sequence, Hybrid Leonardo Sequence, The Binet Formula, Generating Function -
International Journal Of Nonlinear Analysis And Applications, Volume:16 Issue: 2, Feb 2025, PP 245 -253In this research, new representations of basic functions are proposed based on the new types of fuzzy partition and a subnormal generating function. The generalized uniform fuzzy partitions in subnormal case, i.e. in case a generating function K is not normal (generalized normal case), and simpler form of fuzzy transform (FzT) components based on these new representations of the generalized uniform fuzzy partitions are indicated. The main properties of a new uniform fuzzy partition are suggested. New theorems and lemmas are proved.Keywords: Fuzzy Partition, Fuzzy Transform, Basic Function, The Membership Functions, Generating Function, Ruspini Condition
-
The aim of this paper is to introduce the hyperbolic generalized $k$-Horadam quaternions and octonions and investigate their algebraic properties. We present some properties and identities of these quaternions and octonions for generalized $k$-Horadam numbers. Moreover, we give some determinants related to the hyperbolic generalized $k$-Horadam quaternions and octonions. Finally, we evaluate its determinants through the Chebyshev polynomials of the second kind and give an illustrative example as well.Keywords: Horadam Number, Hyperbolic Quaternions, Octonions, Binet Formula, Generating Function, Chebyshev Polynomials
-
We obtain the generating function for the number of columns of fixed height $r$ in a bargraph (classified according to semi-perimeter). As initial case for two distinct methods we first find the generating function for columns of height $1$. Then using a first-return-to-level-$1$ decomposition, we obtain the rational function version of the continued fraction generating function which allows us to derive separate recursions for its numerator and denominator. This then allows us to get the asymptotic average number of columns for each $r$. We also obtain an equivalent generating function by exploiting a sequential decomposition for bargraphs in terms of columns of height $r$.Keywords: generating function, bargraphs, column height
-
The continuous dual Hahn polynomials are orthogonal polynomials in a single variable whose weight function is given by the product of the gamma function. In this paper, we derive some advanced properties for these polynomials including multilinear and multilateral generating functions, recurrence relations and various integral representations.
Keywords: Hypergeometric Series, Continuous DualHahn Polynomials, Generating Function, Recurrence Relation, IntegralRepresentation -
International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 1, Jan 2023, PP 2123 -2128We propose a beta exponential distribution that is formed from the logarithm of a random variable with a beta value, as well as a thorough investigation of the distribution's mathematical characteristics. Because we dealt with the beta exponential distribution, we have a clear and understandable way to comprehend the equation and apply it to the actual problem. To do this, we gathered the questions that statisticians find interesting and studied the most significant properties and statistics related to the distribution. Future research will utilize this data to identify specific industrial flaws or inefficiencies as a function of survival. Included are system statistics, BE distributions for graphs, generation functions, moments, and Hazard functions.Keywords: Hazard function, Moment, Generating Function, shape, Order statistics of BE Distribution
-
In this study, a generalization of the Pell sequence called bi-periodic Pell sequence is carried out to matrix theory. Therefore, we call this matrix sequence the bi-periodic Pell matrix sequence whose entries are bi-periodic Pell numbers. Then the generating function, Binet formula and some basic properties and sum formulas are examined.
Keywords: Pell Sequence, Generating Function, Binet Formula -
A non-empty set S ⊆ V is a dominating set, if every vertex not in S is adjacent to at least one vertex in S, and S is a total dominating set, if every vertex of V is adjacent to some vertices of S. We enumerate dominating sets, non-split dominating sets and total dominating sets in several classes of cactus chains.Keywords: Dominating sets, Total dominating sets, Generating function, Cactus graphs, i-uniform
-
We investigate the eigenvalue distribution of banded Hankel matrices with non-zero skew diagonals. This work uses push-forward of an arcsine density, block structures and generating functions. Our analysis is done by a combination of Chebyshev polynomials, Laplacian determinant expansion and mathematical induction.Keywords: Hankel, eigenvalue, Distribution, generating function
-
In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to de ne new family of generalized Bernoulli polynomials which include Hermite-Bernoulli polynomials introduced by G. Dattoli and al [1].Keywords: Generating function, composition of generating func- tions, composita, Faa di Bruno formula
-
توزیع های آماری در توصیف و پیش بینی پدیده های دنیای واقعی بسیار مفید هستند. انتخاب توزیع آماری مناسب برای مدل سازی داده ها بسیار مهم است. در این مقاله، یک کلاس جدید از توزیع های طول عمر پیشنهاد شده به نام خانواده وایبل تاپ-لیون تعمیم یافته (WTLG) پیشنهاد داده می شود. خانواده پیشنهاد شده از توزیع ها با ترکیب توزیع وایبل با توزیع تاپ- لیون ساخته می شود که می تواند انعطاف بیشتری نسبت به توزیع های طول عمر شناخته شده، داشته باشد. همچنین چندین خواص آماری این خانواده از جمله چگالی و تابع نرخ خطر، رفتار مجانبی، نمایش آمیخته، چولگی و کشیدگی، گشتاورها، تابع مولد گشتاور بیان شده است. برای برآورد پارامترهای آن از روش های مختلف استفاده شده است. مقایسه عملکرد برآوردگرهای پیشنهاد شده در عمل به صورت عددی بررسی شده است. به علاوه آزمون نسبت درسنمایی ماکسیمم را برای این خانواده انجام شده است. در ادامه به کمک شبیه سازی عملکرد برآوردگر درستنمایی ماکزیمم را با محاسبه اریبی و میانگین توان دوم خطا مورد بررسی قرار داده می شود. در انتها بر پایه ی دو نوع داده واقعی انعطاف پذیری خانواده توزیع های هدف نشان داده شده است.
کلید واژگان: تابع مولد، توزیع های طول عمر، برآورد ماکسیمم درستنمایی، توزیع تاپ-لئون، توزیع وایبلStatistical distributions are very useful in describing and predicting real world phenomena. Consequently, the choice of the most suitable statistical distribution for modeling given data is very important. In this paper, we propose a new class of lifetime distributions called the Weibull Topp-Leone Generated (WTLG) family. The proposed family is constructed via compounding the Weibull and the Topp-Leone distributions. It can provide better fits and is very flexible in comparison with the various known lifetime distributions. Several general statistical properties of the WTLG family are studied in details including density and hazard shapes, limit behavior, mixture representation, skewness and kurtosis, moments, moment generating function, incomplete moment. Different methods have been used to estimate its parameters. The performances of the estimators are numerically investigated. We have discussed inference on the new family based on the likelihood ratio statistics for testing some lifetime distributions. We assess the performance of the maximum likelihood estimators in terms of the biases and mean squared errors by means of a simulation study. The importance and flexibility of the new family are illustrated by means of two applications to real data sets.
Keywords: Generating Function, Lifetime Distributions, Maximum Likelihood Estimation, Quantile Function, Topp-Leone Distribution, Weibull Distribution -
رده ی جدیدی از مدل ها به نام خانواده ی وایبول G -تعمیم یافته با دو پارامتر مثبت شکل اضافی پیش نهاد شده است که چندین مدل شناخته شده را تعمیم می دهد. برخی از خواص ریاضی شامل گشتاورهای عادی و ناکامل ، تابع مولد ، آماره های مرتب ، گشتاورهای وزنی احتمال ، آنتروپی ، باقی مانده ها ، و تابع طول عمر باقی مانده ی معکوس به دست آورده شده اند. مشخص سازی بر اساس دو نسبت گشتاورهای بریده شده بر حسب تابع خطر و بر اساس تابع های معینی از متغیر تصادفی ارایه شده است. پارامترهای مدل به وسیله ی روش بیشینه ی درستنمایی براورد شده اند. با استفاده از دو مطالعه ی شبیه سازی کارایی براوردگرهای بیشینه ی درستنمایی بر حسب اریبی و میانگین توان دوم خطا ارزیابی شده اند. مفید بودن مدل های پیش نهادی به وسیله ی سه داده ی واقعی تشریح شده است.کلید واژگان: مدل وایبول، مشخص سازی، آماره های مرتب، براورد بیشینه ی درستنمایی، تابع چندکی، تابع مولد، گشتاورهاWe propose a new class of continuous models called the Weibull Generalized G family with two extra positive shape parameters, which extends several well-known models. We obtain some of its mathematical properties including ordinary and incomplete moments, generating function, order statistics, probability weighted moments, entropies, residual, and reversed residual life functions. Characterizations based on a ratio of two truncated moments, in terms of hazard function and based on certain functions of the random variable are presented. We estimate the model parameters by the maximum likelihood method. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of two simulation studies. The usefulness of the proposed models is illustrated via three real data sets.Keywords: Weibull model, characterizations, order statistics, maximum likelihood estimation, quantile function, generating function, moments
-
Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagons. Furthermore, as corollaries, the expected values of the well-known topological indices: Wiener index, hyper-Wiener index and Tratch-Stankevitch-Zefirov index of a random benzenoid chain with $n$ hexagons can be obtained by simple mathematical calculations, which generates the results given by I. Gutman et al. [Wiener numbers of random benzenoid chains, Chem. Phys. Lett. 173 (1990) 403-408].Keywords: Wiener index, Random benzenoid chain, Hosoya polynomial, Expected value, Generating function
-
We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.Keywords: Tutte polynomial, wheel, fan, generating function
-
Bentea and Tu{a}rnu{a}uceanu~(An. c{S}tiinc{t}. Univ. Al. I. Cuza Iac{s}, Ser. Nouv{a}, Mat., {bf 54(1)} (2008), 209-220) proposed the following problem: Find an explicit formula for the number of fuzzy subgroups of a finite hamiltonian group of type $Q_8times mathbb{Z}_n$ where $Q_8$ is the quaternion group of order $8$ and $n$ is an arbitrary odd integer. In this paper we consider more general group: the direct product of a generalized quaternion group of any even order and a cyclic group of any odd order. For this group we give an explicit formula for the number of fuzzy subgroups.Keywords: Generalized quaternion group, Hamiltonian group, Fuzzy subgroups, Subgroup chain, Generating function
-
Let n β(n) o∞ n=0 be a sequence of positive numbers and 1 < p < ∞. We consider the weighted Hardy space Hp (β). We investigate the relation between the generating function and the functional of point evaluations. Also, under a sufficient condition we determine the structure of all non-zero multiplicative linear functionals on Hp (β).
Keywords: The Banach space of formal powerseries associated with a sequence β, bounded point evaluation, generating function
- نتایج بر اساس تاریخ انتشار مرتب شده‌اند.
- کلیدواژه مورد نظر شما تنها در فیلد کلیدواژگان مقالات جستجو شده‌است. به منظور حذف نتایج غیر مرتبط، جستجو تنها در مقالات مجلاتی انجام شده که با مجله ماخذ هم موضوع هستند.
- در صورتی که می‌خواهید جستجو را در همه موضوعات و با شرایط دیگر تکرار کنید به صفحه جستجوی پیشرفته مجلات مراجعه کنید.
©2000-2025 magiran.com All Rights Reserved.