Sharif Digital Repository

In this paper, we find upper bounds for the eigenvalues of the Laplacian in the conformal class of a compact Riemannian manifold (M,g). These upper bounds depend only on the dimension and a conformal invariant that we call "min-conformal volume". Asymptotically, these bounds are consistent with the Weyl law and improve previous results by Korevaar and Yang and Yau. The proof relies on the construction of a suitable family of disjoint domains providing supports for a family of test functions. This method is interesting for itself and powerful. As a further application of the method we obtain an upper bound for the eigenvalues of the Steklov problem in a domain with C1 boundary in a complete... 

In this paper we prove a new capacity upper bound for a class of relay channels known as Relay-With-Delay channels. The proposed bound is general and holds for any arbitrary amount of delay. We have shown that the previously introduced bounds can be considered as special cases of our proposed upper bound. The new introduced bound is, in some cases, tighter than the previously established bounds. It is also notable that the proposed bound coincides with the previously known capacity of "Relay-With-Delay" channels. © 2009 IEEE  

The interconnection network between the processor cores in multiprocessors on chip has a crucial impact on the performance. Efficient VLSI layout area of such networks can result in lower costs and better performance. Layouts with more compact area can lead in shorter wires and therefore the signal propagation through the wires may take place in shorter time. In this paper, we study the VLSI layout bounds of a new product network, called the Edge Graph Product. Lower bounds are usually computed by the crossing number and bisection width of the topological graphs. For computing the bisection width and crossing number of the edge graph product, we use the obtained upper bound on maximal... 

Thermal behavior and require power in hot continuous strip rolling are predicted by means of a coupled finite element-upper bound approach. A thermal-finite element analysis is utilized to simultaneously determine temperature distributions within the work-piece and the work-rolls while an upper bound solution is employed at the same time to estimate the rate of heat of deformation and the required power in each rolling stand. The proposed model can be applied for determining thermal behaviors of the strip and the work-rolls in single and multi- pass rolling schedules while the effects of different parameters including initial temperature and rolling speed can be considered in the analysis.... 

The purpose of this paper is to develop a mathematical solution to estimate the deformation pattern and required power in cold plate rolling using coupled stream function method and upper bound theorem. Design/methodology/approach-In the first place, an admissible velocity field and the geometry of deformation zone are derived from a new stream function. Then, the optimum velocity field is obtained by minimizing the corresponding power function. Also, to calculate the adiabatic heating during high speed rolling operations, a two-dimensional conduction-convection problem is sequentially coupled with the mechanical model. To verify the predictions, rolling experiments on aluminum plates are... 

In this paper, we study the zero error capacity of the molecular delay channel when multiple molecule types are available at the transmitter. In the molecular delay channel, each transmitted molecule (of any type) is received by a delay of at most k time slots. Depending on the number of molecules that the transmitter is allowed to release in each time slot, we consider the following three cases: (i) when the maximum number of the released molecules of each type in each time slot is restricted (ii) when the total number of the released molecules (regardless of their type) in each time slot is restricted, and (iii) when the transmitter can use only one molecule type (of its choice) in each... 

We consider one-hop communication in wireless networks with random connections. In the random connection model, the channel powers between different nodes are drawn from a common distribution in an i.i.d. manner. In a wireless network with n nodes, a simple one-hop scheme achieving the throughput scaling of order n 1/3-δ, for any arbitrarily small δ > 0, is proposed. This scheme is based on maximizing the number of successful concurrent transmissions. Such achievable throughput, along with the order n 1/3 upper bound derived by Cui et al., characterizes the throughput of one-hop schemes for the class of connection models with distribution having finite mean and variance  

Dilation of a set of points on the plane is the lowest possible dilation of a plane spanner on the point set. We show that dilation of vertices of any regular polygon is less than 1.4482. We introduce a method for constructing a triangulation of a regular polygon and prove this bound on its dilation. The upper bound on dilation is shown using mathematical proofs and experimental results. The new upper bound improves the previously known bound of 1.48454. © 2019 Elsevier B.V  

In this research, deformation of material in equal channel angular extrusion (ECAE) process with outer curved corner is analyzed using an upper bound solution. The effects of die angle, friction between the sample and the die walls, and the angle of the outer curved corner, on the extrusion pressure are all considered in the analysis. It is found that the extrusion pressure decreases with increasing both the die angle and the outer curved corner angle and increases with increasing the friction coefficient. Moreover, a good agreement is found between the predicted and experimental results of extrusion pressure relating to two dies of different outer curved corner angles used in ECAE tests of... 

We give an upper bound on the performance of the belief propagation algorithm in decoding a code over a binary-input output-symmetric channel in terms of the decoding threshold of the code over the erasure channel. Using this upper bound, we obtain the overhead of fountain codes on the erasure channel, provided that they are capacity-achieving on a symmetric channel. The upper bound is similar to a lower bound proved by Khandekar. The lower bound will be used to bound from above the reception overhead of fountain codes on symmetric channels  

Considering a kinematical velocity admissible field, the upper bound method has been used for predicting the amount of pressure in hydroforming of sheet metals. The effects of work hardening, friction and blank size have been considered in pressure prediction. Also the effect of sheet thickness variation has been considered in the present work formulations. The relation between pressure and punch stroke has been obtained and optimized by changing the selective parameters in the velocity components. The results for cylindrical and hemispheric parts have been obtained and compared with the published experimental results. The effects of work hardening, friction and blank size on hydroforming... 

'Help bits' are some limited trusted information about an instance or instances of a computational problem that may reduce the computational complexity of solving that instance or instances. Assume that we can efficiently solve k instances of a decision problem using some help bits whose entropy is less than k when the k instances are drawn independently from a particular distribution. Then there is an upper bound on the average-case complexity of the problem, namely we can efficiently solve an instance drawn from that distribution correctly with probability better than 1/2  

In this paper, we enumerate the number of combinatorial changes of the the Euclidean minimum spanning tree (EMST) of a set of n moving points in 2- dimensional space. We assume that the motion of the points in the plane, is defined by algebraic functions of maximum degree s of time. We prove an upper bound of O(n3β2s(n2)) for the number of the combinatorial changes of the EMST, where βs(n)= λs(n)/n and λs(n) is the maximum length of Davenport-Schinzel sequences of order s on n symbols which is nearly linear in n. This result is an O(n) improvement over the previously trivial bound of O(n4)  

This study deals with the subject of robust bounded-input bounded-output (BIBO)-stability of a family of fractional order interval systems. Employing the idea of'robust stability testing function'and extending it to the case of intended systems, a simple graphical procedure for checking the robust BIBO-stability applicable to both commensurate and incommensurate orders is developed. Moreover, a Kharitonov-like theorem is provided that presents necessary and sufficient conditions for checking the mentioned stability of the fractional order interval systems with commensurate order α belonging to [1,2), but only sufficient conditions for commensurate order α in interval (0,1). Besides, lower... 

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation (Formula presented.) of G for every two adjacent vertices v and u, the sum of incoming edges of v and u in the oriented graph are different from each other. The universal labeling number of a graph G is the minimum number k such that G has universal labeling from (Formula presented.) denoted it by (Formula presented.). We have (Formula presented.), where (Formula presented.) denotes the maximum degree of G. In this work, we offer a provocative question that is: “Is there any polynomial function f such that for every graph G, (Formula presented.)?”. Towards this question, we introduce some... 

Theorem 5 of A. Gohari, V. Anantharam, IEEE Transactions on Information Theory, vol. 56, no. 8, pp. 3973-3996, 2010, states an upper bound on the secrecy capacity for the source model problem. It has a three page proof given in Appendix B of the paper. Unfortunately, we show that this bound does not provide any improvement over the simpler bound given in Corollary 1 of the paper. We also provide an example of a family of two agent source model problems where the one-way secrecy rate in each direction is zero, but the secrecy rate is nonzero and can be determined exactly as a conditional mutual information. © 1963-2012 IEEE  

In some applications, the variance of measurement noise depends on the signal that we aim to measure. For instance, additive Gaussian signal-dependent noise (AGSDN) channel models are used in molecular and optical communication. Herein we provide lower and upper bounds on the capacity of additive signal dependent noise (ASDN) channels. We also provide sufficient conditions under which the capacity becomes infinity. © 2017 IEEE  

Give a triangulation of a set of points on the plane, dilation of any two points is defined as the ratio between the length of the shortest path of these points and their Euclidean distance. Minimum dilation triangulation is a triangulation in which the maximum dilation between any pair of the points is minimized. We give upper bounds on the dilation of the minimum dilation triangulation for two kinds of point sets: An upper bound of nsin⁡(π/n)/2 for a centrally symmetric convex point set containing n points, and an upper bound of 1.19098 for a set of points on the boundary of a semicircle. © 2018 Elsevier B.V  

In this note, we study the behavior of independent sets of maximum probability measure in tensor graph powers. To do this, we introduce an upper bound using measure preserving homomorphisms. This work extends some previous results concerning independence ratios of tensor graph powers. © 2008 Elsevier B.V. All rights reserved