‎The maximum clique problem (MCP) is to determine a complete subgraph of maximum cardinality in a graph‎. ‎MCP is a fundamental problem in combinatorial optimization and is noticeable for its wide range of applications‎. ‎In this paper‎, ‎we present two branch-and-bound exact algorithms for finding a maximum clique in an undirected graph‎. ‎Many efficient exact branch and bound maximum clique algorithms use approximate coloring to compute an upper bound on the clique number but‎, ‎as a new pruning strategy‎, ‎we show that local core number is more efficient‎. ‎Moreover‎, ‎instead of neighbors set of a vertex‎, ‎our search area is restricted to a subset of the set in each subproblem which speeds up clique finding process‎. ‎This subset is based on the core of the vertices of a given graph‎. ‎We improved the MCQ and MaxCliqueDyn algorithms with respect to the new pruning strategy and search area restriction‎. ‎Experimental results demonstrate that the improved algorithms outperform the previous well-known algorithms for many instances when applied to DIMACS benchmark and random graphs‎.

‎In the present paper, we investigate  the eigenvalues of an elliptic differential operator on compact Riemannian manifolds with boundary and derive a general inequality for these eigenvalues. Applying this inequality, we give universal estimates  for eigenvalues on compact domains of  complete submanifolds in an Euclidean space, and of complete manifolds admitting special functions. Finally, we find universal bounds on  the $(k+1)$-th eigenvalue on such objects in terms of the first $k$ eigenvalues independent of  the domains.

For a graph G, the third neighborhood degree index of G is defined as: ND3(G) = X ab∈E(G) δG(a)δG(b)  δG(a) + δG(b) , where δG(a) represents the sum of degrees of all neighboring vertices of vertex a. In this short paper, we establish a new lower bound on the third neighborhood degree index of trees and characterize the extremal trees achieving this bound.

Performance measurement is very important to assessment Banks performance. Data envelopment analysis is one of the performance measurement tools. The purpose of this research is to investigate the efficiency of branches by using data envelopment analysis approach. The research is descriptive-quantitative in terms of purpose, application and nature. Branch entry consists of three variables: cost, number of personnel, amount of outstanding debt to the total loan of each branch. The top banks are far more cost efficient in terms of performance and have a lower amount of outstanding debt than loans. Output variable including absorbed resources, consumption and number of customers for each year compared to prior periods of each item, first with win4deap, GAMS soft with Data analyzed by window approach and efficient branches And inefficiently ranked and ranked accordingly.

Cardiac pacing is the only effective therapy for patients with symptomatic bradycardia in the absence of reversible etiologies. Right ventricular pacing (RVP) has been widely used for almost 60 years. However, RVP causes electric and mechanical dyssynchrony. Due to such effects, RVP is associated with an increased risk of heart failure and atrial fibrillation development. For these reasons, there is increasing interest in physiological pacing techniques that directly activate the specialized conduction system. There are two main methods for conduction system pacing: 1) His Bundle Pacing (HBP) 2) Left Bundle Pacing (LBP) HBP has gained prominence. Multiple studies have demonstrated the feasibility and clinical benefits of this technique...

A five-year-old boy presented to the ophthalmology emergency department with a three-day history of sudden onset of severe visual impairment in both eyes. He experienced an upper respiratory tract infection (URTI) two weeks before the presenting complaint. On initial ophthalmic examination, his visual acuity was hand motion with projection OU. He had no relative afferent pupillary defect, and had normal intraocular pressure. The visual reduction was not associated with pain or injection. Slit-lamp examination of both eyes showed mild anterior chamber (AC) reaction (1–, 2+ cells), moderate bilateral presence of vitreous cells (2–, 3+ cells), but no keratic precipitates....

Traveling Salesman Problem has numerous applications in sequencing and scheduling. Branch exchange heuristic is a quick algorithm which can result in a near optimal solution for symmetrical traveling salesman problem. In this paper an new method for selecting the branch is presented which saves the quality of solvings but results in a decrease of one- third in computational time compare with other branch exchange algorithms.

Bovine Leukosis Virus (BLV) belongs to the genus Deltaretrovirus ,subfamily Orthoretrovirinae of the family Retroviridae comprising 3 main genes of gag, pol and env and a number of replication regulatory genes such as Tax, Rex, R III, C IV. For determination of genetic relationship of Tax gene of BLV in Iran with those in other countries fragments 927bp corresponding to Tax from four infected samples were amplified in PCR system and sequenced for determining nucleotide sequence and compared with identified nucleotide sequence of this gene in other countries.A comparison made on Tax gene in Iran with other countries demonstrated 3.4 to 7.7% variability in Tax gene, of which the greatest sequence similarity exists between sequences of Tax in Iran with USA (AY700378.1)with 96.6% similarity and the least relationship exists between sequences of this virus in Iran with Australia (AY700379.1) and Japan (AY700381.1) with 92.3% similarity.

In today's competitive world, applying new techniques to business development has a great impact. The restaurant industry is no exception. Therefore, in this research, using new methods of knowledge discovery and data mining, customer data of chain restaurant is investigated. The purpose of this study was to explore customer behavior patterns using data mining methods. In this study, one million and five hundred thousand customer records were reviewed in five branches of a chain restaurant and two stages of clustering modeling using RFM method and then classification modeling were performed on the data and the behavior rules chain restaurant customers were extracted. The results of this study have helped to identify the loyal and profitable customers of the chain restaurant which has led to the improvement of the profitability of the chain restaurant. One of the innovations of this research has been the communication between clustering and classification results.