The congruence equation a¯ + b¯ ≡c¯(modp)

2019 ◽  
pp. 1-12
Author(s):  
Tsz Ho Chan
Keyword(s):  
Gauss Sums ◽  
Kloosterman Sums ◽  
The Other ◽  
Number Of Solutions ◽  
Multiplicative Inverse ◽  
Other Hand ◽  
Order Of Magnitude ◽  
Congruence Equation ◽  
First Moment

In this paper, we consider the congruence equation [Formula: see text] with [Formula: see text] where [Formula: see text] denotes the multiplicative inverse of [Formula: see text]. We prove that its number of solutions is asymptotic to [Formula: see text] when [Formula: see text] by estimating a certain average of Kloosterman sums via Gauss sums. On the other hand, when [Formula: see text], the number of solutions has order of magnitude at least [Formula: see text]. It would be interesting to better understand its transition of behavior. By transforming the question slightly, one can relate the problem to a certain first moment of Dirichlet [Formula: see text]-functions at [Formula: see text].

Comparison of the Potency of 8-L-Arginine, 8-D-Arginine and 8-D-Homoarginine Vasopressin Analogs with Substituted Phenylalanine in Position 2

1994 ◽  
Vol 59 (6) ◽  
pp. 1439-1450 ◽  
Author(s):  
Miroslava Žertová ◽  
Jiřina Slaninová ◽  
Zdenko Procházka
Keyword(s):  
Amino Acid ◽  
Solid Phase Synthesis ◽  
Solid Phase ◽  
Basic Amino Acid ◽  
The Other ◽  
Side Chain ◽  
Inhibitory Potency ◽  
Phase Synthesis ◽  
Other Hand ◽  
Order Of Magnitude

An analysis of the uterotonic potencies of all analogs having substituted L- or D-tyrosine or -phenylalanine in position 2 and L-arginine, D-arginine or D-homoarginine in position 8 was made. The series of analogs already published was completed by the solid phase synthesis of ten new analogs having L- or D-Phe, L- or D-Phe(2-Et), L- or D-Phe(2,4,6-triMe) or D-Tyr(Me) in position 2 and either L- or D-arginine in position 8. All newly synthesized analogs were found to be uterotonic inhibitors. Deamination increases both the agonistic and antagonistic potency. In the case of phenylalanine analogs the change of configuration from L to D in position 2 enhances the uterotonic inhibition for more than 1 order of magnitude. The L to D change in position 8 enhances the inhibitory potency negligibly. Prolongation of the side chain of the D-basic amino acid in position 8 seems to decrease slightly the inhibitory potency if there is L-substituted amino acid in position 2. On the other hand there is a tendency to the increase of the inhibitory potency if there is D-substituted amino acid in position 2.

The No-Three-In-Line Problem

1968 ◽  
Vol 11 (4) ◽  
pp. 527-531 ◽  
Author(s):  
Richard K. Guy ◽  
Patrick A. Kelly
Keyword(s):  
Finite Number ◽  
The Other ◽  
Probabilistic Argument ◽  
Number Of Solutions ◽  
Other Hand ◽  
Image Position

Let Sn be the set of n2 points with integer coordinates n (x, y), 1 ≤ x, y <n. Let fn be the maximum cardinal of a subset T of Sn such that no three points of T are collinear. Clearly fn < 2n.For 2 ≤ n ≤ 10 it is known ([2], [3] for n = 8, [ 1] for n = 10, also [4], [6]) that fn = 2n, and that this bound is attained in 1, 1, 4, 5, 11, 22, 57, 51 and 156 distinct configurations for these nine values of n. On the other hand, P. Erdös [7] has pointed out that if n is prime, fn ≥ n, since the n points (x, x2) reduced modulo n have no three collinear. We give a probabilistic argument to support the conjecture that there is only a finite number of solutions to the no-three-in-line problem. More specifically, we conjecture that

Interactions of LO Phonons with Bound Excitons in Homoepitaxial GaN

1997 ◽  
Vol 482 ◽  
Author(s):  
K. P. Koron ◽  
A. Wysmolek ◽  
J. M. Baranowskil ◽  
K. Pakul ◽  
J. P. Bergman ◽  
...  
Keyword(s):  
Temperature Dependence ◽  
The Other ◽  
Direct Influence ◽  
Neutral Donor ◽  
Phonon Replica ◽  
Temperature Range ◽  
Other Hand ◽  
Order Of Magnitude ◽  
Neutral Acceptor

AbstractPhotoluminescence connected with excitons and their phonon replicas in undoped homoepitaxial MOCVD grown GaN layers have been studied in the temperature range 2 - 100 K. It is shown that the coupling between LO phonons and neutral acceptor bound excitons (ABE) is much stronger than the coupling between LO phonons and neutral donor bound excitons (DBE). In spite that emission due the DBE no-phonon is one order of magnitude stronger than the ABE one, the predominant feature of the first LO phonon replica of the excitonic structures is related to the ABE. It is argued that this fact is connected with delocalization of the acceptor wavefunction in the k-space which leads to a higher number of interacting LO phonons in the first replica. On the other hand, the second LO phonon replica of the excitonic structures is predominantly connected with the DBE. In the case of two LO phonons interacting with bound excitons the k - conservation has not so direct influence. In addition, the temperature dependence of LO phonon replicas and their kinetics in ps regime are also reported.

A PDL APPROACH FOR QUALITATIVE VELOCITY

2011 ◽  
Vol 19 (01) ◽  
pp. 11-26 ◽  
Author(s):  
A. BURRIEZA ◽  
E. MUÑOZ-VELASCO ◽  
M. OJEDA-ACIEGO
Keyword(s):  
Programming Languages ◽  
Moving Objects ◽  
Spatial Reasoning ◽  
Axiom System ◽  
Qualitative Reasoning ◽  
The Other ◽  
Other Hand ◽  
Order Of Magnitude ◽  
The One ◽  
Different Levels

We introduce the syntax, semantics, and an axiom system for a PDL-based extension of the logic for order of magnitude qualitative reasoning, developed in order to deal with the concept of qualitative velocity, which together with qualitative distance and orientation, are important notions in order to represent spatial reasoning for moving objects, such as robots. The main advantages of using a PDL-based approach are, on the one hand, all the well-known advantages of using logic in AI, and, on the other hand, the possibility of constructing complex relations from simpler ones, the flexibility for using different levels of granularity, its possible extension by adding other spatial components, and the use of a language close to programming languages.

scholarly journals Accelerated sliding of pollen tube organelles along Characeae actin bundles regulated by Ca2+.

1988 ◽  
Vol 106 (5) ◽  
pp. 1539-1543 ◽  
Author(s):  
T Kohno ◽  
T Shimmen
Keyword(s):  
Heat Treatment ◽  
Pollen Tube ◽  
Cytoplasmic Streaming ◽  
Pollen Tubes ◽  
The Other ◽  
Cell Models ◽  
Organelle Movement ◽  
Actin Bundles ◽  
Other Hand ◽  
Order Of Magnitude

Pollen tubes show active cytoplasmic streaming. We isolated organelles from pollen tubes and tested their ability to slide along actin bundles in characean cell models. Here, we show that sliding of organelles was ATP-dependent and that motility was lost after N-ethylmaleimide or heat treatment of organelles. On the other hand, cytoplasmic streaming in pollen tube was inhibited by either N-ethylmaleimide or heat treatment. These results strongly indicate that cytoplasmic streaming in pollen tubes is supported by the "actomyosin"-ATP system. The velocity of organelle movement along characean actin bundles was much higher than that of the native streaming in pollen tubes. We suggested that pollen tube "myosin" has a capacity to move at a velocity of the same order of magnitude as that of characean myosin. Moreover, the motility was high at Ca2+ concentrations lower than 0.18 microM (pCa 6.8) but was inhibited at concentration higher than 4.5 microM (pCa 5.4). In conclusion, cytoplasmic streaming in pollen tubes is suggested to be regulated by Ca2+ through "myosin" inactivation.

scholarly journals One kind power mean of the hybrid Gauss sums

2018 ◽  
Vol 16 (1) ◽  
pp. 531-538
Author(s):  
Qi Lan ◽  
Zhang Wenpeng
Keyword(s):  
Exact Formula ◽  
Gauss Sums ◽  
Computational Formula ◽  
Analysis Method ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Number Of Solutions ◽  
Computational Problem ◽  
Congruence Equation

AbstractIn this paper, we use the analysis method and the properties of trigonometric sums to study the computational problem of one kind power mean of the hybrid Gauss sums. After establishing some relevant lemmas, we give an exact computational formula for it. As an application of our result, we give an exact formula for the number of solutions of one kind diagonal congruence equation modp, wherepbe an odd prime.

The Secular and the Religious

2020 ◽  
pp. 111-134
Author(s):  
Syafiq Hasyim
Keyword(s):  
Public Sphere ◽  
Religion And Politics ◽  
The Other ◽  
Modern State ◽  
Nation State ◽  
Muslim Society ◽  
Other Hand ◽  
Total Separation ◽  
First Moment ◽  
Secular State

Chapter four highlights two crucial issues that modern Indonesia has faced as a nation state: a systematic and passionate inclusion of Sharia into the legal and public sphere of this country (Shariatization), and secularization, applied to guard Indonesia, which fulfils the standard of a democratic modern state. These two are problematic considering Indonesia is neither an Islamic nor a secular State. As a non-theocratic State, in fact, Indonesia remains unable to completely stop several efforts of Shariatization promoted by some groups of Muslim society, and as non-secular State, Indonesia cannot adopt a total separation of religion and politics either. This chapter traces the first moment of Indonesia adopting Sharia on one hand and selecting compatible aspects of secularism on the other hand, and analyses how both are maintained in the configuration of the Indonesian nation state.

STUDY OF METHYLENE BLUE INTERACTION WITH SYNTHETIC POLYNUCLEOTIDE POLY(rA)-POLY(rU)

2020 ◽  
Vol 54 (2 (252)) ◽  
pp. 112-117
Author(s):  
M.A. Parsadanyan ◽  
M.A. Shahinyan ◽  
A.P. Antonyan
Keyword(s):  
Methylene Blue ◽  
Fluorescence Spectroscopy ◽  
The Other ◽  
Binding Modes ◽  
Other Hand ◽  
Non Linear ◽  
Order Of Magnitude ◽  
Synthetic Polynucleotide ◽  
Specific Ligand

A study of the interaction of methylene blue (MB) with poly(rA)-poly(rU) by the method of fluorescence spectroscopy has been carried out. The data obtained revealed that MB, being a DNA-specific ligand, can bind to double-stranded regions of RNA. In this regard, as in the case of DNA, semi-intercalation was the most preferable mechanism for the binding of this ligand to poly(rA)-poly(rU). On the other hand, non-linear curves of dependence of F0/F on concentration of polynucleotide might result from two binding modes, the second of which was probably of an electrostatic nature. Proceeding from the data obtained, the value of KSV was revealed to be almost an order of magnitude less than for DNA, which may indicate that RNA is a less preferable target for MB.

scholarly journals THE SPECTRAL SEQUENCE OF BLAZARS — STATUS AND PERSPECTIVES

2008 ◽  
Vol 17 (09) ◽  
pp. 1457-1466 ◽  
Author(s):  
L. MARASCHI ◽  
G. GHISELLINI ◽  
F. TAVECCHIO ◽  
L. FOSCHINI ◽  
R. M. SAMBRUNA
Keyword(s):  
Spectral Sequence ◽  
Present Status ◽  
The Other ◽  
Lower Power ◽  
Original Idea ◽  
Other Hand ◽  
New Findings ◽  
Order Of Magnitude ◽  
Γ Rays ◽  
Magnitude Increase

The present status of the blazar spectral sequence is discussed, including new findings about blazars selected with different criteria than the original complete radio-samples. Despite extensive searches of blazars "breaking" the sequence, the original idea proposed 10 years ago still seems to hold. On the other hand, the forthcoming launch of the GLAST satellite will provide a new selection band for blazars and blazar related populations as well as fantastic progress on the spectra and variability behaviour of presently known blazars. The order of magnitude increase in sensitivity of GLAST will allow detection of γ-rays from jets with lower power and/or lower beaming factor, thus sampling a much wider population.

scholarly journals The IAU Nutation Theory and Perspectives of its Change

1995 ◽  
Vol 10 ◽  
pp. 247-248
Author(s):  
D. McCarthy ◽  
V. Dehant
Keyword(s):  
Celestial Mechanics ◽  
Analytical Theory ◽  
The Other ◽  
General Assembly ◽  
Other Hand ◽  
Order Of Magnitude ◽  
Rigid Earth ◽  
The One ◽  
Nutation Series ◽  
Whole Earth

The IAU General Assembly has adopted in 1980 a nutation series, on the one hand, based on rigid Earth’s contributions theorically computed from celestial mechanics, and on the other hand, based on non-rigid Earth’s contributions theoretically computed from Earth deformation equations using geophysical parameters.1.From the previous papers (see Session 1) of this Joint Discussion, we know that there are differences of this adopted theory with respect to the observations of precession and nutations. These differences can reach several mas, which is well above the present accuracy of the observations.2.From previous papers (see Session 2) and from the posters, we also know that there exist new rigid-Earth nutations (Kinoshita-Souchay, Roosbeek, Hartmann) of which the accuracy has increased by one order of magnitude.3.From Session 3 papers, we know that there are some additional geophysical effects that are not yet taken into account in Wahr’s nutation theory adopted in 1980 by the IAU which have a contribution at a level above the present precision of the observations. These additional geophysical aspects can be accounted for either from a semi-analytical theory (like Mathews, Herring, Shapiro and Buffett are doing), or from an integration of deformation equations through the whole Earth (Dehant, Wahr).

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