Modules in which every surjective endomorphism has a $$\mu $$-small kernel

2020 ◽  
Vol 66 (2) ◽  
pp. 325-337
Author(s):  
Abderrahim El Moussaouy ◽  
M’Hammed Ziane
Keyword(s):  
Small Kernel

On the short surface waves due to a half-immersed circular cylinder oscillating on water of infinite depth

1982 ◽  
Vol 384 (1787) ◽  
pp. 333-357 ◽  
Keyword(s):  
Circular Cylinder ◽  
Surface Waves ◽  
Usual Method ◽  
Two Dimensional ◽  
Infinite Depth ◽  
Small Kernel ◽  
Rolling Mode ◽  
Incident Waves ◽  
Plausible Argument ◽  
Fixed Cylinder

In this paper we examine two-dimensional short surface waves in water of infinite depth produced by various modes of oscillation of a half-immersed circular cylinder. The usual method, which depends on finding the potential on the cylinder from an integral equation with a small kernel, is here replaced by one that uses instead the known value of the potential for incident waves in the presence of the fixed cylinder. Thus we are able to determine three-term asymptotic expansions for both the heaving and the swaying modes that improve on earlier forms, and, for the heaving mode, to refine the interpolation with previous numerical calculations and confirm in principle the result obtained elsewhere by a plausible argument. The rolling mode also can actually be included by superposition of the heaving and swaying modes for this cylinder.

Epimorphisms in the Category of ℓ-Groups

2009 ◽  
Vol 16 (01) ◽  
pp. 123-130
Author(s):  
Xinmin Lu ◽  
Hourong Qin
Keyword(s):  
Proper Subclass ◽  
Small Kernel

In the category of ℓ-groups, we introduce the concepts of Hopfian and generalized Hopfian ℓ-groups. An ℓ-group G is called Hopfian if every surjective ℓ-homomorphism f : G → G is an ℓ-isomorphism, and G is called generalized Hopfian if every surjective ℓ-homomorphism f : G → G has a small kernel in G. By an example we show that the class of generalized Hopfian ℓ-groups is a proper subclass of Hopfian ℓ-groups. In this paper, we establish some characterizations for them, which generalize some results in [9].

scholarly journals A Study on Rupture Resistance of Groundnut (cv. SAMNUT 22) Kernel

2021 ◽  
Vol 2 (1) ◽  
pp. 19-33
Author(s):  
Hilary UGURU ◽  
Ovie Isaac AKPOKODJE ◽  
Ebubekir ALTUNTAS
Keyword(s):  
Loading Rate ◽  
International Standards ◽  
Medium Size ◽  
Maturity Stage ◽  
Processing Unit ◽  
Mechanical Parameters ◽  
Rupture Force ◽  
Kernel Size ◽  
Small Kernel ◽  
Large Kernel

This study was done to assess the influence of compression loading rate and kernel size on the rupture resistance of groundnut (cv. SAMNUT 22) kernel. These groundnut kernel mechanical parameters (rupture force, deformation at rupture, rupture power, firmness and toughness) were evaluated under three loading rates (15 mm min-1, 20 mm min-1 and 25 mm min-1), and three size categories (small, medium and large). The groundnut kernels were harvested at peak maturity stage, and tested in accordance to ASTM International standards. Results obtained from the tests showed that the rupture resistance of SAMNUT 22 kernel was highly dependent on its size and the loading rate. Generally, as the loading rate increases, the mechanical parameters values declined significantly (p ≤ 0.05). Rupture force, deformation at rupture point, rupture power and the firmness increased as the kernel size increases; but in contrast, the kernel toughness decreases as its size increased. An average force of 57.96 N ruptured the large kernel, while a lower force of 27.35 N ruptured the small kernel. Moreover, the large kernel recorded the highest firmness (59.03 N mm-1), when compared to the medium (51.69 N mm-1) and small (44.98 N mm-1) size kernel. In terms of rupture power, the small kernel power ranged from 0.1002 W (15 mm min-1) to 0.084 W (25 mm min-1); medium size kernel ranged from 0.115 W (15 mm min-1) to 0.074 W (25 mm min- 1); while the large size kernel ranged from 0.135 W (15 mm min-1) to 0.104 W (25 mm min-1). These results portrayed importance of sorting of the groundnut kernels before processing unit operation, as it will help to conserve power and energy during the processing operation.

scholarly journals A Kernel-Width Adaption Diffusion Maximum Correntropy Algorithm

2020 ◽  
Author(s):  
Ying Guo ◽  
Bing Ma ◽  
Yingsong Li
Keyword(s):  
Steady State ◽  
Impulse Noise ◽  
Kernel Width ◽  
Sparse System ◽  
Initial Stage ◽  
Small Kernel ◽  
Sparse Systems ◽  
Simulation Results ◽  
Maximum Correntropy Criterion ◽  
Large Kernel

In this paper, a diffusion maximum correntropy criterion (DMCC) algorithm with adaption kernel width is proposed, denoting as DMCC$_{\rm adapt}$ algorithm, to find out a solution for dynamically choosing the kernel width. The DMCC$_{\rm adapt}$ algorithm chooses small kernel width at initial stage to improve its convergence speed rate, and uses large kernel width at completion stage to reduce its steady-state error. To render the proposed DMCC$_{\rm adapt}$ algorithm suitable for sparse system identifications, the DMCC$_{\rm adapt}$ algorithm based on proportional coefficient adjustment is realized and named as diffusion proportional maximum correntropy criterion (DPMCC$_{\rm adapt}$). The theoretical analysis and simulation results are presented to show that the DPMCC$_{\rm adapt}$ and DMCC$_{\rm adapt}$ algorithms have better convergence than the traditional diffusion AF algorithms under impulse noise and sparse systems.

scholarly journals Essentially Retractable Modules Relative To A Submodule And Some Generalizations

2021 ◽  
Author(s):  
Shukur Neamah Al-Aeashi ◽  
Fatimah Hussein Al-Bakaa
Keyword(s):  
Basic Properties ◽  
Small Kernel ◽  
Unitary Right

R is a ring with unity, and all modules are unitary right R-modules. The concept of compressible modules was introduced in 1981 by Zelmanowitz, where module M is called compressible if it can be embedded in any nonzero submodule A of M . In other words, M is a compressible module if for each nonzero submodule A of M, f 2 Hom(M;A) exists, such that f is monomorphism. Retractable modules were introduced in 1979 Khuri, where module M is retractable if Hom(M, A ) 6= 0 for every nonzero submodule A of M . We define a new notion, namely, essentially retractable module relative to a submodule. In addition, new generalizations of compressible modules relative to a submodule are introduced, where module M is called compressible module relative to a submodule N of M . If for all nonzero submodule K of M contains N , then a monomorphism f 2 Hom(M, K) exists. Some basic properties are studied and many relationships between these classes and other related concepts are presented and studied. We also introduce another generalization of retractable module, which is called small kernel retractable module

Ecogeographic and genetic determinants of kernel weight and colour of wild barley (Hordeum spontaneum) populations in Israel

2004 ◽  
Vol 14 (2) ◽  
pp. 137-146 ◽  
Author(s):  
Guoxiong Chen ◽  
Tatiana Suprunova ◽  
Tamar Krugman ◽  
Tzion Fahima ◽  
Eviatar Nevo
Keyword(s):  
Molecular Markers ◽  
Wild Barley ◽  
Size Variation ◽  
Hordeum Spontaneum ◽  
Kernel Weight ◽  
Phenotypic Traits ◽  
Genetic Determinants ◽  
Ecological Stress ◽  
Colour Category ◽  
Small Kernel

The aim of this study was to establish associations of kernel weight and colour with ecogeographic factors and molecular markers, based on ten wild barley [Hordeum spontaneum (C. Koch) Thell.] populations sampled in Israel across a southward transect of increasing aridity. Kernel weight and colour category were scored using barley kernels (naked caryopsis). Small kernel sizes (0.011 g kernel–1) and dark kernels were found in xeric populations. A higher variation of kernel weight was observed in xeric populations. A higher proportion of variation occurred within, rather than among, populations. Water, temperature and soil factors were associated with kernel size variation. Among 18 simple sequence repeats (SSRs) investigated, HVM14, HVM36, HVM43, BMS64 and BMS90 were associated with kernel weight, and HVM68 with kernel colour. The results indicated that high phenotypic variation and genetic diversity are related to ecological stress, and that the association of phenotypic traits with molecular markers, based on natural plant populations, should be interpreted cautiously due to the high chance of spurious associations between traits and molecular markers.

Two-dimensional oscillations in a canal of arbitrary cross-section

1965 ◽  
Vol 61 (3) ◽  
pp. 827-846 ◽  
Author(s):  
A. M. J. Davis
Keyword(s):  
Integral Equation ◽  
Cross Section ◽  
Arbitrary Cross Section ◽  
Inviscid Fluid ◽  
Degenerate Kernel ◽  
Two Dimensional ◽  
Small Kernel ◽  
Uniform Cross Section ◽  
Set Up ◽  
Image Position

AbstractAn infinitely long canal with uniform cross-section is filled with inviscid fluid. It is required first to show that any small two-dimensional motion of the fluid can be represented as the superposition of normal mode disturbances. A suitable generalized Green's function G(x, y; ξ) is constructed and is used to set up an integral equation (2·9) for the velocity potential on the free surface. It is shown that the eigenfunctions are complete and so are their (possibly time-dependent) extensions to the whole canal, in the sense that an arbitrary disturbance possesses a unique representation. In section 5, it is required to find asymptotic approximations to the large eigenvalues of (2·9). For this purpose a different integral equation (5·5) is set up on the canal, the kernel of which is the sum of a degenerate kernel and a small kernel. The solutions of this equation can therefore be obtained by iteration. The form of the mth eigenvalue is shown to befor sufficiently large m.

On the short-wave asymptotic theory of the wave equation (∇2 + k2)ø = 0

1957 ◽  
Vol 53 (1) ◽  
pp. 115-133 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Asymptotic Expansion ◽  
Green’S Function ◽  
Green's Function ◽  
Short Wave ◽  
Regularity Conditions ◽  
Convex Curve ◽  
Normal Velocity ◽  
Sound Waves ◽  
Small Kernel ◽  
Image Position

ABSTRACTThe theory of time-periodic wave problems falls into two parts. On the one hand there is the rigorous formulation in terms of differential wave equations, on the other there are approximate theories like geometrical optics. It should be possible, in principle, to deduce the latter from the former by a logical process; but this has been done only for a few simple configurations, e.g. the circle. A possible approach to the solution of the general problem is suggested here, and is applied to a typical two-dimensional acoustical example. An arbitrary closed convex curve (satisfying certain regularity conditions) is emitting short sound waves towards infinity, the normal velocity V(s) exp (− iωt) is prescribed on the curve as a function of the arc-length s, and the potential is to be found, first on the curve and then at any point in the sound field. (Only the first part of the problem is treated in detail.) The potential ø(s) exp (− iωt) on the curve satisfies all the integral equationswhere G(s, s′) is any Green's function of the problem, and V(a) is prescribed. All the equations corresponding to different Green's functions have the same solution. An asymptotic and convergent short-wave solution can be found by iteration if G can be chosen explicitly so that the integral equation has a small kernel for high frequencies. At any point of the curve draw the local circle of curvature; then the explicit known solution for a source on this circle is (with slight modifications) a possible Green's function, and the equation formed with it has a small kernel and can be solved rigorously by iteration. If V(a) is independent of the frequency, the leading term in the resulting asymptotic expansion iswhere c is the velocity of sound and 2πk−1 is the (short) wavelength corresponding to the frequency ω/2π. If V(a) varies rapidly, as in diffraction theory, the iterative solution still gives a convergent asymptotic expansion, but the first approximation is then practically useless in the shadow region. Diffraction problems are not treated in the present paper.The present work appears to be the first practical and rigorous solution of a short-wave problem in optics or acoustics when a solution in closed form is not available. It is suggested that the technique (suitably combined with formal expansions) may be applicable to a wider class of radiation and diffraction problems.

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