Sub-Weyl strength bounds for twisted GL(2)GL(2) short character sums

Let $$S(N) = \sum_{n \sim N}^{\text{smooth}} \, \lambda_{f}(n) \, \chi(n),$$ where $\lambda_{f}(n)$'s are Fourier coefficients of Hecke-eigen form, and $\chi$ is a primitive character of conductor $p^{r}$. In this article we prove a sub-Weyl strength bounds for $S(N)$. Indeed, we obtain $$S(N) \ll \, N^{\frac{5}{9}} \ p^{\frac{13r}{45}},$$ provided that $p^{13r/20} \leq N \leq p^{4r/5}$. Note that the above bound for $S(N)$ is non-trivial if $N\geq \left(p^{r}\right)^{\frac{2}{3}-\frac{1}{60}}$.Comment: First draf

Hybrid method for achieving Pareto front on economic emission dispatch

In this paper hybrid method, Modified Nondominated Sorted Genetic Algorithm (MNSGA-II) and Modified Population Variant Differential Evolution(MPVDE) have been placed in effect in achieving the best optimal solution of Multiobjective economic emission load dispatch optimization problem. In this technique latter, one is used to enforce the assigned percent of the population and the remaining with the former one. To overcome the premature convergence in an optimization problem diversity preserving operator is employed, from the tradeoff curve the best optimal solution is predicted using fuzzy set theory. This methodology validated on IEEE 30 bus test system with six generators, IEEE 118 bus test system with fourteen generators and with a forty generators test system. The solutions are dissimilitude with the existing metaheuristic methods like Strength Pareto Evolutionary Algorithm-II, Multiobjective differential evolution, Multi-objective Particle Swarm optimization, Fuzzy clustering particle swarm optimization, Nondominated sorting genetic algorithm-II

Morpho-physiological changes in oil palm (Elaeis guineensis Jacq.) tenera hybrid seedlings raised under different shade levels

Climatic conditions prevailing in oil palm growing states of India indicate the need for shade during primary stage of oil palm nursery for optimum growth and vigour of seedlings. Experiments were conducted to standardize the shade requirement based on growth/quality of oil palm seedlings in summer, rainy and winter seasons by providing 25%, 50% and 75% ultra violet stabilized high density poly ethylene (HDPE) shade nets. Results were found significant among the treatments for most of the growth parameters studied over the seasons. Highergrowth for key characters like seedling height, leaf area, collar girth and dry matter production were recorded at 75% shade level. Similarly, higher chlorophyll content, photosynthetic rate, transpiration rate, stomatal conductance and inter cellular CO2 concentration were observed at 75% shade. Among the season, seedling growth was vigorous in rainy season followed by summer and winter seasons. Hence, provision of 75% shade found to be ideal for raising seedlings during primary stage of nursery in oil palm

Sub-convexity bound for GL(3)×GL(2)GL(3) \times GL(2) LL-functions: GL(3)GL(3)-spectral aspect

Let $\phi$ be a Hecke-Maass cusp form for $SL(3, \mathbb{Z})$ with Langlands parameters $({\bf t}_{i})_{i=1}^{3}$ satisfying $$|{\bf t}_{3} - {\bf t}_{2}| \leq T^{1-\xi -\epsilon}, \quad \, {\bf t}_{i} \approx T, \quad \, \, i=1,2,3$$ with $1/2 0$. Let $f$ be a holomorphic or Maass Hecke eigenform for $SL(2,\mathbb{Z})$. In this article, we prove a sub-convexity bound $$L(\phi \times f, \frac{1}{2}) \ll \max \{ T^{\frac{3}{2}-\frac{\xi}{4}+\epsilon} , T^{\frac{3}{2}-\frac{1-2 \xi}{4}+\epsilon} \}$$ for the central values $L(\phi \times f, \frac{1}{2})$ of the Rankin-Selberg $L$-function of $\phi$ and $f$, where the implied constants may depend on $f$ and $\epsilon$. Conditionally, we also obtain a subconvexity bound for $L(\phi \times f, \frac{1}{2})$ when the spectral parameters of $\phi$ are in generic position, that is $${\bf t}_{i} - {\bf t}_{j} \approx T, \quad \, \text{for} \, i \neq j, \quad \, {\bf t}_{i} \approx T , \, \, i=1,2,3.$$Comment: First draf

A New Approach for Transition Metal Free Magnetic Sic: Defect Induced Magnetism After Self-ion Implantation

SiC has become an attractive wide bandgap semiconductor due to its unique physical and electronic properties and is widely used in high temperature, high frequency, high power and radiation resistant applications. SiC has been used as an alternative to Si in harsh environments such as in the oil industry, nuclear power systems, aeronautical, and space applications. SiC is also known for its polytypism and among them 3C-SiC, 4H-SiC and 6H-SiC are the most common polytypes used for research purposes. Among these polytypes 4H-SiC is gaining importance due to its easy commercial availability with a large bandgap of 3.26 eV at room temperature. Controlled creation of defects in materials is an approach to modify the electronic properties in a way that new functionality may result. SiC is a promising candidate for defect-induced magnetism on which spintronic devices could be developed. The defects considered are of room temperature stable vacancy types, eliminating the need for magnetic impurities, which easily diffuse at room temperature. Impurity free vacancy type defects can be created by implanting the host atoms of silicon or carbon. The implantation fluence determines the defect density, which is a critical parameter for defect induced magnetism. Therefore, we have studied the influence of low fluence low energy silicon and carbon implantation on the creation of defects in n-type 4H-SiC. The characterization of the defects in these implanted samples was performed using the techniques, RBS-channeling and Raman spectroscopy. We have also utilized these characterization techniques to analyze defects created in much deeper layers of the SiC due to implantation of high energy nitrogen ions. The experimentally determined depths of the Si damage peaks due to low energy (60 keV) Si and C ions with low fluences (< 1015 cm-2) are consistent with the SRIM-2011 simulations. From RBS-C Si sub-lattice measurements for different fluences (1.1×1014 cm-2 to 3.2×1014 cm-2) of Si implantation in 4H-SiC, the Si vacancy density is estimated to range from 1.29×1022 cm-3 to 4.57×1022 cm-2, corresponding to average vacancy distances of 4.26 Å to 2.79 Å at the damage peak (50±5 nm). Similarly, for C implanted fluences (1.85×1014 cm-2 to 1×1015 cm-2), the Si vacancy density varies from 1.37×1022 cm-3 to 4.22×1022 cm-3 with the average vacancy distances from 4.17 Å to 2.87 Å at the damage peak (110±10 nm). From the Raman spectroscopy, the implantation-induced lattice disorders calculated along the c-axis (LO mode) and perpendicular to c-axis (TO mode) in 4H-SiC are found to be similar. Furthermore, the results obtained from SQUID measurements in C implanted n-type 4H-SiC sample with fluences ranging from 1×1012 to 1.7×1016 ions/cm2 have been discussed. The implanted samples showed diamagnetism similar to the unimplanted sample. To date, to our best of knowledge, no experimental work has been reported on investigating defect induced magnetism for self-ion implantation in n-type 4H-SiC. These first reports of experimental results can provide useful information in future studies for a better understanding of self-ion implantation in SiC-based DMS