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In Honor and Memory of Professor Lajos Takács
No full textThis 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 come up with a solution to resolve this paradox. In response, I received an e-mail from Dalma, his wife, that broke down me to tears by the sad news she broke that he passed away on the day I sent my e-mail. I am extremely sorry for the loss of such a great human being, teacher, scholar and a world-leading scientist. He was my teacher, mentor and loving professor Lajos Takács. However, we are consoled by the belief that he is alive and well among the world’s mathematics and science society forever. I am sure he is at peace. He has my prayers. I cannot say more about him than what I had prepared to present in his honor as a Preface to the AAM Vol. 10, Issue 2 (December 2015). I am talking about a humble human being, a mentor, a caring teacher, a brilliant Hungarian mathematician, scientist, probabilist, statistician, a pioneer of queueing theory, honored by many organizations, a winner many prizes, including the John von Neumann Theory prize, and doctoral dissertation guide of 23 students, including Paul Burke and myself. The impact of his 225 original papers and his two books, Introduction to the Theory of Queues and Combinatorial Methods in Theory of Stochastic Processes is tremendous. One could not imagine what the impact of his 1600 unpublished materials on the theory of random fluctuation would be on the theory of probability. While I was writing about his famous Integro-Differential Equation in chapter 5 of my book and reviewing the literature, I noticed that this 1962 formula was applied by Hága et al. (2006) regarding an Efficient and reliable available bandwidth measurement. Another paper I came to notice was by Kim (2014) regarding an available server management in the Internet connected network environments, in which local backup servers are hooked up by LAN and remote backup servers are hooked up by VPN (Virtual Private Network) with high-speed optical network citing Takács (1958), Theory of Telephone Traffic. So, it is not only that his 1962 book has been cited hundreds of times, but even his older papers are also being used these days. The rest of this Preface was presented at the The 8th International Conference on Lattice Path Combinatorics and Applications, on August 18, 2015, at California Polytechnic State University Pomona, California, United States of America, at his 91st birthday, in honor of Professor Lajos Takács. The presentation was made jointly by Professors Aliakbar Montzer Haghighi and Sri Gopal Mohanty
Stability Condition of a Retrial Queueing System with Abandoned and Feedback Customers
Get PDFThis paper deals with the stability of a retrial queueing system with two orbits, abandoned and feedback customers. Two independent Poisson streams of customers arrive to the system, and flow into a single-server service system. An arriving one of type i; i = 1; 2, is handled by the server if it is free; otherwise, it is blocked and routed to a separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. The customer in the orbit either attempts service again after a random time or gives up receiving service and leaves the system after a random time. After the customer is served completely, the customer will decide either to join the retrial group again for another service or leave the system forever with some probability
Differential Transform Method for Solving the Two-dimensional Fredholm Integral Equations
Get PDFIn this paper, we develop the Differential Transform (DT) method in a new scheme to solve the two-dimensional Fredholm integral equations (2D-FIEs) of the second kind. The differential transform method is a procedure to obtain the coefficients of the Taylor expansion of the solution of differential and integral equations. So, one can obtain the Taylor expansion of the solution of arbitrary order and hence the solution of the given equation can be obtained with required accuracy. Here, we first give some basic definitions and properties about DT from references, and then we prove some theorems to extend the DT method for solving the 2D-FIEs. Then by using the DT, the 2D-FIE is converted to a system of linear algebraic equations whose unknowns are the coefficients of the Taylor expansion of the solution. Solving the system gives us an approximate solution. Finally, we give some examples to show the accuracy and efficiency of the presented method
Mathematical Modeling of Two-dimensional Unsteady Flow in Growing Tumor
Get PDFWe investigate the problem of unsteady fluid flow in growing solid tumors. We develop a mathematical model for a growing tumor whose boundary is taken as a sphere, and the unsteady fluid flow within the tumor is assumed to be two dimensional with respect to the radial distance and the latitudinal angle in spherical coordinates. The expressions for the time, radial and latitudinal variations of the flow velocity, pressure, and the two investigated drug concentrations within the tumor were determined analytically. We calculated these quantities in the tumor as well as in a corresponding normal tissue. We find, in particular, that blood pressure in the tumor would be higher than that in the normal tissue, and there could be blood flow circulation in the tumor. For a given spatial location in the tumor, the amount of drug delivered to the growing tumor decreases first with time, but then the rate of decrease reduces with further increase in time. The Therapeutic Index, which is a measure of the efficiency of drug delivery in the tumor in the biomedical science, is determined for different values of the parameters and discussed in the absence or presence of the drugs’ interactions which may exist in the presence of the two drugs in the tumor. The main results of our model agree with the available experiments
On Some Optimal Multiple Root-Finding Methods and their Dynamics
Get PDFFinding multiple zeros of nonlinear functions pose many difficulties for many of the iterative methods. In this paper, we present an improved optimal class of higher-order methods for multiple roots having quartic convergence. The present approach of deriving an optimal class is based on weight function approach. In terms of computational cost, all the proposed methods require three functional evaluations per full iteration, so that their efficiency indices are 1.587 and, are optimal in the sense of Kung-Traub conjecture. It is found by way of illustrations that they are useful in high precision computing enviroments. Moreover, basins of attraction of some of the higher-order methods in the complex plane are also given
Non-mosaic monosomy 59,X in cattle: a case report
No full textA 3-year-old Longhorn heifer was referred to the Veterinary Medical Teaching Hospital of Texas A&M University for inability to get pregnant. Physical examination revealed a small-sized female for age and breed with a normal vulva, vaginal length, and external cervical os. Further assessment by per rectum palpation and trans-rectal ultrasonography revealed a small uterine cervix and cord-like uterine horns with no identifiable ovaries. Additional evaluation including laparoscopy, hormonal evaluation, and genetic analysis allowed ruling out conditions commonly associated with a phenotypic female with infantile or underdeveloped reproductive organs such as freemartin, XY gonadal dysgenesis, testicular feminization, and bilateral ovarian agenesis. Laparoscopy confirmed the presence of a small cervix with small uterine horns and absence of ovaries. Testosterone, progesterone, and 17-β estradiol concentrations were 200.0pg/mL, 1.48ng/mL, and undetectable, respectively. Genetic evaluation determined that the karyotype was 59,X non-mosaic. Evaluation of phenotypically female cattle with infertility and infantile genital organs and absence of ovaries should include cytogenetic analysis to test for possible X monosomy. The 59,X condition should be considered in the differential diagnoses together with freemartin, dysgenesis XY, testicular feminization, and bilateral ovarian agenesis
Strong Uniform Consistency of Hazard Function with Functional Explicatory Variable in Single Functional Index Model under Censored Data
Get PDFIn this paper we deal with nonparametric estimate of the conditional hazard function, when the covariate is functional. Kernel type estimators for the conditional hazard function of a scalar response variable Y given a Hilbertian random variable X are introduced, where the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence (with the rate) of the kernel estimate of this model in various situations, including censored and non-censored data. The rates of convergence emphasize the crucial role played by the small ball probabilities with respect to the distribution of the explanatory functional variable