Average behavior of the triple divisor function over values of quadratic form

2020 ◽  
Author(s):  
Guangwei Hu ◽  
Weiwei Hu
Keyword(s):  
Quadratic Form ◽  
Divisor Function ◽  
Average Behavior

EVALUATION OF CONVOLUTION SUMS AND FOR k = a · b = 21, 33, AND 35

2021 ◽  
pp. 1-20
Author(s):  
K. PUSHPA ◽  
K. R. VASUKI
Keyword(s):  
Positive Integer ◽  
Quadratic Form ◽  
Eisenstein Series ◽  
Modular Forms ◽  
Divisor Function ◽  
Convolution Sums

Abstract The article focuses on the evaluation of convolution sums $${W_k}(n): = \mathop \sum \nolimits_{_{m < {n \over k}}} \sigma (m)\sigma (n - km)$$ involving the sum of divisor function $$\sigma (n)$$ for k =21, 33, and 35. In this article, our aim is to obtain certain Eisenstein series of level 21 and use them to evaluate the convolution sums for level 21. We also make use of the existing Eisenstein series identities for level 33 and 35 in evaluating the convolution sums for level 33 and 35. Most of the convolution sums were evaluated using the theory of modular forms, whereas we have devised a technique which is free from the theory of modular forms. As an application, we determine a formula for the number of representations of a positive integer n by the octonary quadratic form $$(x_1^2 + {x_1}{x_2} + ax_2^2 + x_3^2 + {x_3}{x_4} + ax_4^2) + b(x_5^2 + {x_5}{x_6} + ax_6^2 + x_7^2 + {x_7}{x_8} + ax_8^2)$$ , for (a, b)=(1, 7), (1, 11), (2, 3), and (2, 5).

On the Number of Divisors of the Quadratic Form m2 + n2

2000 ◽  
Vol 43 (2) ◽  
pp. 239-256 ◽  
Author(s):  
Gang Yu
Keyword(s):  
Asymptotic Behavior ◽  
Quadratic Form ◽  
Real Number ◽  
Positive Real Number ◽  
Divisor Function ◽  
Positive Real ◽  
Number Of Divisors

AbstractFor an integer n, let d(n) denote the ordinary divisor function. This paper studies the asymptotic behavior of the sumIt is proved in the paper that, as x → ∞,where A1 and A2 are certain constants and ε is any fixed positive real number.The result corrects a false formula given in a paper of Gafurov concerning the same problem, and improves the error claimed by Gafurov.

Efektifitas Pendidikan Kesehatan Dengan Metode Ceramah Tentang Vulva Hygiene Terhadap Perilaku Merawat Vulva Hygiene Saat Menstruasi Pada Remaja Putri Kelas VII Di SMPN 1 Gondang Mojokerto

2018 ◽  
Vol 6 (1) ◽  
Author(s):  
Titin Dwi Ernawati ◽  
Nikhen Fitrianingtyas Harni ◽  
Jinnani Firdausiyah
Keyword(s):  
Health Education ◽  
Young Women ◽  
Sampling Technique ◽  
Mean Value ◽  
Measurement Tool ◽  
Test Design ◽  
Average Behavior ◽  
Lecture Method ◽  
Before And After ◽  
Post Test

ABSTRAKWanita muda cenderung memiliki perilaku buruk pada kebersihan selama menstruasi. Ketika reproduksi basah dan basah, maka akan meningkatkan keasaman memfasilitasi pertumbuhan jamur. Kondisi seperti gatal pada vulva, area eksternal biasanya terjadi pada wanita muda di masa menstruasi. Perilaku seseorang dipengaruhi oleh tingkat pendidikan dan pengetahuan. Pengetahuan seseorang tentang sesuatu dapat menyebabkan perubahan perilaku. Tujuan penelitian ini adalah untuk menganalisis efektivitas pendidikan kesehatan dengan metode ceramah dalam merawat kebersihan vulva terhadap perilaku kebersihan vulva saat menstruasi pada wanita muda di kelas VII di SMPN 1 Gondang Mojokerto.Jenis penelitian ini adalah pre eksperimental One Group Pre-Post Test Design. Populasi adalah wanita muda di kelas VII di SMPN 1 Gondang Mojokerto. Teknik pengambilan sampel menggunakan total sampling dan diperoleh 21 sampel wanita muda. Alat ukur yang digunakan dalam penelitian ini adalah kuesioner. Analisis data dengan membandingkan perilaku rata-rata memperlakukan kebersihan vulva selama menstruasi sebelum dan sesudah kuliah pendidikan kesehatan.Hasil penelitian sebelum pengobatan (pre-test) menunjukkan nilai rata-rata 9,000 sedangkan penelitian setelah perawatan (post test) menunjukkan nilai rata-rata 14,190. Ada perubahan dalam perilaku rata-rata memperlakukan kebersihan vulva selama menstruasi wanita muda sebelum dan sesudah kuliah pendidikan kesehatan di 5.190.Berdasarkan hasil pendidikan kesehatan dengan metode ceramah efektif untuk meningkatkan perawatan perilaku untuk kebersihan vulva selama menstruasi pada wanita muda. Kuliah pendidikan kesehatan tentang kebersihan vulva dapat digunakan sebagai salah satu cara efektif untuk memperbaiki perilaku kebersihan yang buruk selama menstruasi pada wanita muda.Kata kunci: pendidikan kesehatan, perilaku, kebersihan vulva ABSTRACTYoung women tend to have bad behavior on hygiene during menstruation. When reproduction moist and wet, it will increase the acidity facilitate mold growth. Conditions such as itching of the vulva, the external area usually occurs during young women in the menstrual period. Person's behavior is influenced by the level of education and knowledge. One's knowledge about something can cause behavioral changes. The purpose of the study was to analyze the effectiveness of health education with the lecture method of treating vulva hygiene on the behavior of vulva hygiene during menstruation in young women in class VII at SMPN 1 Gondang MojokertoType of research is pre experimental One Group Pre-Post Test Design. The population was young women in class VII at SMPN 1 Gondang Mojokerto. Sampling technique used total sampling and obtained 21 samples of young women. Measurement tool used in the study was questionnaire. Analysis of the data by comparing the average behavior of treating vulva hygiene during menstruation before and after the health education lecture.The results of the study before treatment (pre-test) showed a mean value of 9,000 while the study after treatment (post test) showed a mean value of 14,190. There is a change in the average behavior of treating vulva hygiene during menstruation young women before and after the health education lecture at 5,190.Based on the results of health education with the lecture method effectively to improved behavioral care for vulva hygiene during menstruation in young women. Health education lecture about hygiene vulva can be used as one of the effective ways to improve the behavior of poor hygiene during menstruation in young women.Key Words: health education, behaviour, vulva hygiene 

Spheric radial basis functions in Mahalanobis measuring for displaying local field features

2019 ◽  
Vol 952 (10) ◽  
pp. 2-9
Author(s):  
Yu.M. Neiman ◽  
L.S. Sugaipova ◽  
V.V. Popadyev
Keyword(s):  
Gravitational Field ◽  
Quadratic Form ◽  
Local Field ◽  
Euclidean Distance ◽  
Basis Functions ◽  
Spherical Functions ◽  
Local Models ◽  
Stationary Field ◽  
Modeling Process ◽  
The Earth

As we know the spherical functions are traditionally used in geodesy for modeling the gravitational field of the Earth. But the gravitational field is not stationary either in space or in time (but the latter is beyond the scope of this article) and can change quite strongly in various directions. By its nature, the spherical functions do not fully display the local features of the field. With this in mind it is advisable to use spatially localized basis functions. So it is convenient to divide the region under consideration into segments with a nearly stationary field. The complexity of the field in each segment can be characterized by means of an anisotropic matrix resulting from the covariance analysis of the field. If we approach the modeling in this way there can arise a problem of poor coherence of local models on segments’ borders. To solve the above mentioned problem it is proposed in this article to use new basis functions with Mahalanobis metric instead of the usual Euclidean distance. The Mahalanobis metric and the quadratic form generalizing this metric enables us to take into account the structure of the field when determining the distance between the points and to make the modeling process continuous.

scholarly journals Flexible planning of corrective responses for double-step reduction in the number of potential targets

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ryoji Onagawa ◽  
Kazutoshi Kudo
Keyword(s):  
Control System ◽  
Weighted Average ◽  
Double Step ◽  
Average Behavior ◽  
Potential Target ◽  
Flexible Planning ◽  
Corrective Response

AbstractHumans are often required to plan/execute movements in the presence of multiple motor targets simultaneously. Under such situations, it is widely confirmed that humans frequently initiate movements towards the weighted average direction of distinct motor plans toward each potential target. However, in situations where the potential targets change in a step-by-step manner, the strategy to proceed towards the weighted average direction at each time could be sub-optimal in light of the costs of the corrective response. Herein, we tested the sensorimotor strategy followed during a step-by-step reduction of potential goals. To test the hypothesis, we compared the corrective responses when the number of targets went from three to two, and when the number of targets went from three to one at the same time. As the results, weak corrections were confirmed when the number of targets was reduced from three to two. Moreover, the corrective responses when the number of targets went from three to two was smaller than the average behavior estimated from the corrective responses when the number of targets went from three to one at the same time. This pattern of corrective responses reflects the suppression of unnecessary corrections that generate noise and cost to the control system. These results suggest that the corrective responses are flexibly modulated depending on the necessity, and cannot be explained by weighted average behavior.

scholarly journals A BOUND FOR THE INDEX OF A QUADRATIC FORM AFTER SCALAR EXTENSION TO THE FUNCTION FIELD OF A QUADRIC

2018 ◽  
Vol 19 (2) ◽  
pp. 421-450 ◽  
Author(s):  
Stephen Scully
Keyword(s):  
Quadratic Form ◽  
Upper Bound ◽  
Function Field ◽  
The Other ◽  
Direct Generalization ◽  
Other Hand ◽  
General Field ◽  
The One ◽  
Anisotropic Quadratic Form

Let $q$ be an anisotropic quadratic form defined over a general field $F$. In this article, we formulate a new upper bound for the isotropy index of $q$ after scalar extension to the function field of an arbitrary quadric. On the one hand, this bound offers a refinement of an important bound established in earlier work of Karpenko–Merkurjev and Totaro; on the other hand, it is a direct generalization of Karpenko’s theorem on the possible values of the first higher isotropy index. We prove its validity in two key cases: (i) the case where $\text{char}(F)\neq 2$, and (ii) the case where $\text{char}(F)=2$ and $q$ is quasilinear (i.e., diagonalizable). The two cases are treated separately using completely different approaches, the first being algebraic–geometric, and the second being purely algebraic.

scholarly journals An Inhomogeneous Minimum For Non-Convex Star-Regions With Hexagonal Symmetry

1955 ◽  
Vol 7 ◽  
pp. 337-346 ◽  
Author(s):  
R. P. Bambah ◽  
K. Rogers
Keyword(s):  
Quadratic Form ◽  
Binary Quadratic Form ◽  
Elementary Geometry ◽  
Hexagonal Symmetry ◽  
Real Numbers ◽  
Inhomogeneous Minimum ◽  
Image Position ◽  
Indefinite Binary Quadratic Form

1. Introduction. Several authors have proved theorems of the following type:Let x0, y0 be any real numbers. Then for certain functions f(x, y), there exist numbers x, y such that1.1 x ≡ x0, y ≡ y0 (mod 1),and1.2 .The first result of this type, but with replaced by min , was given by Barnes (3) for the case when the function is an indefinite binary quadratic form. A generalisation of this was proved by elementary geometry by K. Rogers (6).

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