Quantitative Version of the Oppenheim Conjecture for Inhomogeneous Quadratic Forms

A quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms is proved. We also give an application to eigenvalue spacing on flat 2-tori with Aharonov-Bohm flux

Quasinormal modes in kink excitations and kink-antikink interactions: a toy model

We study excitations and collisions of kinks in a scalar field theory where the potential has two minima with $Z_2$ symmetry. The field potential is designed to create a square well potential in the stability equation of the kink excitations. The stability equation is analogous to the Schr\"{o}dinger equation, and therefore we use quantum mechanics techniques to study the system. We modify the square well potential continuously, which allows the excitation to tunnel and consequently turns the normal modes of the kink into quasinormal modes. We study the effect of this transition, leading to energy leak, on isolated kink excitations. Finally, we investigate kink-antikink collisions and the resulting scaling and fractal structure of the resonance windows considering both normal and quasinormal modes and compare the results.Comment: 23 pages, 11 figure

The Relationship of Conformity and Memory

Some theorists believe that the brain was evolved under the influence of the community and for the community. So it seems that social function has priority on pure cognitive in the brain. The purpose of this research was to study the relationship between conformity and general memory. The current study is a descriptive-correlational research by using prediction (regression) method. For doing this, 167 students were selected via the multistage cluster method from Bonab and Tabriz Payam Noor universities. For gathering data, the Conformity L-72 Test and general memory Questionnaire (PRMQ) were used. The data were analyzed by using Pearsons Correlation test and Liner Regression methods. According to the results, the predictive role of conformity for errors in the general memory was confirmed (P<0/01). So that conformity explained 46% of general memory errors variance. Based on these results, it seems that social and cognitive functions of the brain are linked together to meet common goals.Keywords: Conformity, General Memory, Social Brain, Cognitio

Effects of weight and length of Barbus grypus broodstock on fingerlings production and growth

The effects of weight and length of Barbus grypus broodstock on fingerlings reproductive characteristics and growth were investigated. We chose three female treatments including weight and length groups (1) 2212.5±479g, 62.68±6.7cm, (2) 4518±780g, 79.12±4.36cm and (3) 7712.5±1171g, 92.62±3.13cm. The same male broodstock were used for all the treatments with the weight and length size of 1400±100g, 54.62±7.35cm. Female broodstock were injected 3mg/kg PG hormone two times at an interval of 10 hours. Males were injected 2mg/kg once at the time females received their second injection. Larvae and fingerling survival rate and growth indices (special growth coefficient, condition factor) up to the fingerling stage were calculated for all treatments of larvae culture. Fingerling stage in ponds, 02, pH, temperature, transparency, nitrate, and phosphate were measured and no significant difference was observed (P>0.05) among the ponds. The special growth rate, condition factor, and fingerling survival of the treatments showed no significant differences (P>0.05). However, our results indicated that larvae survival rate had significant differences between treatment 2 and other treatments (P<0.05). These indices increase in broodstock weight up to treatment 2 (4518±780g, 79.12±4.36cm) and after that it will be lowered. We conclude that the treatment 2 broodstock are ideal for fingerling survival and enhancement of growth and condition factors

Makespan minimizing on multiple travel salesman problem with a learning effect of visiting time

-The multiple traveling salesman problem (MTSP) involves the assignment and sequencing procedure simultaneously. The assignment of a set of nodes to each visitors and determining the sequence of visiting of nodes for each visitor. Since specific range of process is needed to be carried out in nodes in commercial environment, several factors associated with routing problem are required to be taken into account. This research considers visitors’ skill and category of customers which can affect visiting time of visitors in nodes. With regard to learning-by-doing, visiting time in nodes can be reduced. And different class of customers which are determined based on their potential purchasing of power specifies that required time for nodes can be vary. So, a novel optimization model is presented to formulate MTSP, which attempts to ascertain the optimum routes for salesmen by minimizing the makespan to ensure the balance of workload of visitors. Since this problem is an NP-hard problem, for overcoming the restriction of exact methods for solving practical large-scale instances within acceptable computational times. So, Artificial Immune System (AIS) and the Firefly (FA) metaheuristic algorithm are implemented in this paper and algorithms parameters are calibrated by applying Taguchi technique. The solution methodology is assessed by an array of numerical examples and the overall performances of these metaheuristic methods are evaluated by analyzing their results with the optimum solutions to suggested problems. The results of statistical analysis by considering 95% confidence interval for calculating average relative percentage of deviation (ARPD) reveal that the solutions of proposed AIS algorithm has less variation and Its’ confidence interval of closer than to zero with no overlapping with that of FA. Although both proposed meta-heuristics are effective and efficient in solving small-scale problems, in medium and large scales problems, AIS had a better performance in a shorter average time. Finally, the applicability of the suggested pattern is implemented in a case study in a specific company, namely Kalleh

Collisions between kinks with long-range tails: a simple and efficient method

We construct initial configurations for the scattering between kinks with long-range tails. For this purpose, we exploit kink solutions in the presence of BPS-preserving impurities. This approach offers a highly efficient method and effortless implementation with a negligible computational cost. Our algorithm has a much smaller complexity than the usual minimization method, becoming more than a hundred times faster in some scenarios. Consequently, conducting kink-antikink simulations becomes remarkably straightforward