Sum of squares

Part 1 of ebook "Proofs from the book" provides readers with contents including: number theory; geometry; six proofs of the infinity of primes; bertrand’s postulate; binomial coefficients are (almost) never powers; representing numbers as sums of two squares; the law of quadratic reciprocity; every finite division ring is a field; hilbert’s third problem - decomposing polyhedra; lines in the plane and decompositions of graphs; the slope problem;...

126p hanlinhchi 29-08-2023 6 2   Download

Continued part 1, part 2 of ebook "A pythagorean introduction to number theory: Right triangles, sums of squares, and arithmetic" has presents the following content: advanced topics; counting pythagorean triples modulo an integer; how many lattice points are there on a circle or a sphere; what about geometry; another proof of the four squares theorem; quadratic forms and sums of squares; how many pythagorean triples are there; how are rational points distributed, really;...

143p dieptieuung 20-07-2023 4 3   Download

Part 1 of ebook "A pythagorean introduction to number theory: Right triangles, sums of squares, and arithmetic" has presents the following content: foundational material; basic number theory; integral solutions to the pythagorean equation; what integers are areas of right triangles; what numbers are the edges of a right triangle; primes of the form 4k+1; gauss sums, quadratic reciprocity, and the jacobi symbol;...

143p dieptieuung 20-07-2023 4 2   Download

This research proposes a new method to synthesize a robust observer for the polynomial systems in the presence of the uncertainties. Here, a special mathematical transformation is carried out to convert the uncertain polynomial systems into the unknown input polynomial systems and then the robust observer is designed for estimating the state variables of these systems.

8p vidoctorstrange 06-05-2023 4 4   Download

In this paper, we propose a novel algorithm to optimize the weighted total system rate (WSR) for a broadcast communication system using multiple input-multiple output (MIMO) antenna technology based on the Harris Hawking Optimization (HHO) algorithm, called Algorithm 1, using the Minimum Mean Square Error (MMSE) filter at the mobile stations (MS).

8p vigeneralmotors 13-07-2022 32 6   Download

This study deals with the adsorption of two pesticides, carbendazim and flumetsulam, from aqueous solutions onto four homoionic-montmorillonite clays (Ag+, Zn2+, Cu 2+, and H+). Equilibrium adsorption isotherm data were analyzed using Freundlich, Dubinin–Radushkevich, and Temkin isotherms. Linear and nonlinear fitting methods were compared to determine the best-fitting isotherms for the experimental data. Three error analysis methods were used to evaluate the data for each method: the coefficient of determination (R2), sum of squared errors (SSE), and chi-square test (χ2).

11p tudichquannguyet 29-11-2021 8 1   Download

The dissertation has four chapters: Chapter 1 - Background Materials; Chapter 2 - Analysis of an Algorithm in Indefinite Quadratic Programming; Chapter 3 - Qualitative Properties of the Minimum Sum-of-Squares Clustering Problem; Chapter 4 - Some Incremental Algorithms for the Clustering Problem.

142p armyofthedead 23-06-2021 31 2   Download

A field experiment was conducted to estimate the genetic variability, trait association and path coefficient analysis among the Indian mustard genotypes during rabi, 2019. Analysis of variance revealed the mean sum of squares due to genotypes was highly significant for all the characters studies indicating the existence of ample variability among the genotypes studied. The high GCV and PCV observed for number of siliquae per plant and secondary branches per plant indicated the influence of environment on the expression of these characters were at minimum level.

12p chauchaungayxua11 23-03-2021 16 2   Download

Thuộc tính địa chấn biên độ trung bình bình phương (Root Mean Square Amplitude), biên độ cực đại (Maximum Amplitude), và tổng biên độ dương (Sum of Positive Amplitude) phản ảnh đặc điểm phân bố của trầm tích cacbonat ám tiêu Miocen giữa, khu vực lô 04-3, bể Nam Côn Sơn một cách rõ rệt nhất. Cacbonat Miocen giữa phân bố phổ biến ở hai mặt phản xạ P1và P2, trong phạm vi mỗi mặt phản xạ, trầm tích cacbonat tập trung ở xung quanh các đới nâng, điển hình như các cấu tạo Thiên Ưng – Mãng Cầu, Đại Hùng và Bồ Câu.

10p larachdumlanat129 14-01-2021 29 3   Download

Present study was conducted with 10 parents, their 45 hybrids along with 4 checks viz., Pratap QPM Hybrid-1, Vivek QPM-9, HQPM-1 and HQPM-5 to estimate GCA and SCA of parents and crosses respectively in diallel mating design (excluding reciprocal crosses) in two environments (Kharif 2014 and Rabi 2014-15) at the Instructional farm, Rajasthan College of Agriculture, MPUAT, Udaipur. Two characters viz.

13p gaocaolon9 22-12-2020 14 2   Download

The present investigation conducted with the using 40 genotypes of vegetable pea to study the extent of variability and genetic divergence among the genotypes for growth yield and quality attributes. The study was conducted in the Randomized block design with 3 replications. The study revealed that mean sum of squares due to genotypes for 18 quantitative characters was highly significant for all traits indicating ample variation among the genotypes.

5p chauchaungayxua8 03-10-2020 15 2   Download

The analysis of variance for female and male parents exhibited (Table 1) significant difference for all the traits. The estimates of mean sum of squares due to Lines showed significant differences for all the traits except fruit rind thickness, fruit flesh thickness, fruit girth, total soluble solids (TSS) and total crude fiber content and in the male parents apart from these traits node to first female flower, sex ratio, vine length also indicating the presence of sufficient variability among the parents studied.

8p caygaocaolon7 18-09-2020 11 1   Download

Thirty basmati rice genotypes were evaluated in RBD with three replications with an objective of assessing the genetic variability, heritability, genetic advance for twenty-two yield and quality characters. The results of ANOVA revealed that the mean sum of squares among the genotypes for all the characters were highly significant indicating the presence of ample amount of variability which can be exploited for selection of characters for crop improvement programme.

8p nguaconbaynhay7 15-08-2020 15 1   Download

The present investigation was carried out involving thirty hybrids which were derived by crossing ten lines with three testers. These hybrids were evaluated along with their parents in randomized block design (RBD) with three replications. The recorded data was subjected to Line × Tester analysis. The analysis of variance for combining ability revealed that the mean sum of squares due to parents and hybrids were highly significant for almost all the characters except for days required to 50% pistillate flowering, vine length, number of primary branches per plant and internodal length.

9p angicungduoc6 22-07-2020 13 2   Download

The present investigation was carried out at Main Experiment Station, Department of Vegetable Science, Narendra Deva University of Agriculture & Technology, Kumarganj, Faizabad (U.P.) during summer season, to evaluate the available germplasms for yield and its component traits of 45 genotypes, with three replications in Randomized Block Design. The study revealed that the mean sum squares due to genotypes were significant for all the characters, though the wide range of genetic variability in the material.

6p chauchaungayxua6 26-06-2020 15 1   Download

In the recent time, pumpkin has got industrial importance with the development of pulp powder as a nutraceutical supplement to Vitamin A requirement. Pumpkin is cheaper source of Vitamin A when compared to carrot which necessitates specific climatic requirement for its production and high productivity per unit area. An experiment was conducted at the Department of Vegetable Crops, Horticulture College and Research Institute, Tamil Nadu Agricultural University, Coimbatore to find out suitable pumpkin genotype for earliness, high yield and quality.

6p chauchaungayxua6 26-06-2020 14 1   Download

Line x Tester analysis was carried out for thirteen diversified parents at the department of Horticulture, Agricultural College and Research Institute, Madurai, Tamil Nadu, to study the combining ability for yield and yield contributing characters in snake gourd. The analysis for combining ability revealed significant mean sum of squares of both general combining ability (GCA) and specific combining ability (SCA) for all the characters which indicate that the presence of both additive and non-additive gene actions.

6p nguaconbaynhay6 24-06-2020 16 1   Download

The study was carried out at Agricultural Research Station, Tandur (PJTSAU) during Rabi, 2017-18 to determine genetic variability, heritability and genetic advance estimates in thirty genotypes of safflower. Analysis of variance involving a set of thirty genotypes of safflower for seven quantitative characters viz., days to 50% flowering, days to maturity, plant height, number of effective capitula/plant, number of seeds/capitulum, test weight (g) and seed yield (kg/ha) revealed highly significant mean sum of squares for all the characters indicating greater diversity among the genotypes.

5p nguaconbaynhay6 23-06-2020 10 0   Download

Ninty green chickpea (Cicer arietinum L.) genotypes were evaluated for genetic potential, heritability, genetic advance, and traits association of yield contributing characters during 2016-2017 at ARS Kalaburgi, University of agricultural science Raichur, Karnataka, India. The experiment was carried out in augmented design; data were recorded on days to 50% flowering, pods per plant, seeds per pod, number of primary branches /plant, number of secondary branches/ plant, 100-seed weight and seed yield /plant.

8p quenchua6 15-06-2020 18 2   Download

Twenty four newly developed maize hybrids along with three commercial checks were evaluated for their yield performance at three locations under heat stress and optimal conditions. Pooled analysis of variance revealed significant differences among hybrids for grain yield. Mean sum of squares due to environments and linear component of environments were significant for all the traits studied.

9p angicungduoc5 14-06-2020 13 0   Download