scholarly journals On tropical matrices of small factor rank

2012 ◽  
Vol 437 (11) ◽  
pp. 2727-2732 ◽  
Author(s):  
Yaroslav Shitov
Keyword(s):  
Small Factor

scholarly journals Annihilating dark matter search with 12 yr of Fermi LAT data in nearby galaxy clusters

2021 ◽  
Vol 502 (3) ◽  
pp. 4039-4047
Author(s):  
Charles Thorpe-Morgan ◽  
Denys Malyshev ◽  
Christoph-Alexander Stegen ◽  
Andrea Santangelo ◽  
Josef Jochum
Keyword(s):  
Dark Matter ◽  
Galaxy Clusters ◽  
Gamma Ray ◽  
Nearby Galaxy ◽  
Galactic Latitude ◽  
Dark Matter Search ◽  
Dwarf Spheroidal Galaxies ◽  
Characteristic Signal ◽  
Small Factor ◽  
The Impact

ABSTRACT Galaxy clusters are the largest virialized objects in the Universe and, as such, have high dark matter (DM) concentrations. This abundance of dark matter makes them promising targets for indirect DM searches. Here we report the details of a search, utilizing almost 12 yr of Fermi/LAT data, for gamma-ray signatures from the pair annihilation of WIMP dark matter in the GeV energy band. From this, we present the constraints on the annihilation cross-section for the $b\overline{b}$, W+W−, and γγ channels, derived from the non-detection of a characteristic signal from five nearby, high Galactic latitude, galaxy clusters (Centaurus, Coma, Virgo, Perseus, and Fornax). We discuss the potential of a boost to the signal due to the presence of substructures in the DM haloes of selected objects, as well as the impact of uncertainties in DM profiles on the presented results. We assert that the obtained limits are, within a small factor, comparable to the best available limits of those based on Fermi/LAT observations of dwarf spheroidal galaxies.

Randomized sampling and sparsity: Getting more information from fewer samples

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB173-WB187 ◽  
Author(s):  
Felix J. Herrmann
Keyword(s):  
Compressive Sensing ◽  
Sampling Method ◽  
New Technology ◽  
Seismic Exploration ◽  
Transform Domain ◽  
Sampled Data ◽  
Randomized Sampling ◽  
Seismic Acquisition ◽  
Small Factor ◽  
Incoherent Sampling

Many seismic exploration techniques rely on the collection of massive data volumes that are subsequently mined for information during processing. Although this approach has been extremely successful in the past, current efforts toward higher-resolution images in increasingly complicated regions of the earth continue to reveal fundamental shortcomings in our workflows. Chiefly among these is the so-called “curse of dimensionality” exemplified by Nyquist’s sampling criterion, which disproportionately strains current acquisition and processing systems as the size and desired resolution of our survey areas continue to increase. We offer an alternative sampling method leveraging recent insights from compressive sensing toward seismic acquisition and processing for data that are traditionally considered to be undersampled. The main outcome of this approach is a new technology where acquisition and processing related costs are no longer determined by overly stringent sampling criteria, such asNyquist. At the heart of our approach lies randomized incoherent sampling that breaks subsampling related interferences by turning them into harmless noise, which we subsequently remove by promoting transform-domain sparsity. Now, costs no longer grow significantly with resolution and dimensionality of the survey area, but instead depend only on transform-domain sparsity. Our contribution is twofold. First, we demonstrate by means of carefully designed numerical experiments that compressive sensing can successfully be adapted to seismic exploration. Second, we show that accurate recovery can be accomplished for compressively sampled data volumes sizes that exceed the size of conventional transform-domain data volumes by only a small factor. Because compressive sensing combines transformation and encoding by a single linear encoding step, this technology is directly applicable to acquisition and to dimensionality reduction during processing. In either case, sampling, storage, and processing costs scale with transform-domain sparsity. We illustrate this principle by means of number of case studies.

Interface closure in the root region of steady deep-cellular growth in directional solidification

2015 ◽  
Vol 26 (3) ◽  
pp. 355-382 ◽  
Author(s):  
J.-J. XU ◽  
Y.-Q. CHEN
Keyword(s):  
Directional Solidification ◽  
Interfacial Energy ◽  
Turning Point ◽  
Quantization Condition ◽  
Cellular Growth ◽  
Physical Parameters ◽  
Trapped Waves ◽  
Root Region ◽  
Small Factor

The present paper investigates the mechanism of interface closure in the root region of the solutions for steady deep-cellular growth. This phenomenon is determined by a transcendentally small factor beyond all orders. It is found that the root region comprises three inner-inner regions; the inner system in the root region has a simple turning point, whose presence generates the so-called trapped-waves mechanism, which is responsible for the interface closure at the bottom of root. The quantization condition derived from the trapped-waves mechanism yields the eigenvalue that determines the location of interface closure and its dependence on the interfacial energy and other physical parameters.

scholarly journals CONSTRUCTION OF STABILITY AREAS FOR CONTROLLED SYSTEMS WITH PARAMETRIC AND DYNAMIC UNCERTAINTY

2021 ◽  
pp. 117-122
Author(s):  
Alla Savranska ◽  
Oleksandr Denisenko
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Small Parameter ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Systems Of Differential Equations ◽  
Right Hand ◽  
Perturbed Systems ◽  
Small Factor ◽  
The Right

The subject of research in the article is sigularly perturbed controllable systems of differential equations containing terms with a small parameters on the right-hand side, which are not completely known, but only satisfy some constraints. The aim of the work is to expand the study of the behavior of solutions of singularly perturbed systems of differential equations to the case when the system is influenced not only by dynamic (small factor at the derivative) but also parametric (small factor at the right side of equations) uncertainties and to determine conditions under which such systems will be asymptotically resistant to any perturbations, estimate the upper limit of the small parameter, so that for all values of this parameter less than the obtained estimate, the undisturbed solution of the system was asymptotically stable. The following problems are solved in the article: singularly perturbed systems of differential equations with regular perturbations in the form of terms with a small parameter in the right-hand sides, which are not fully known, are investigated; an estimate is made of the areas of asymptotic stability of the unperturbed solution of such systems, that is, the class of systems that can be investigated for stability is expanded, the formulas obtained that allow one to analyze the asymptotic stability of solutions to systems even under conditions of incomplete information about the perturbations acting on them. The following methods are used: mathematical modeling of complex control systems; vector Lyapunov functions investigation of asymptotic stability of solutions of systems of differential equations. The following results were obtained: an estimate was made for the upper bound of a small parameter for sigularly perturbed systems of differential equations with fully known parametric (fully known) and dynamic uncertainties, such that for all values of this parameter less than the obtained estimate, such an unperturbed solution is asymptotically stable; a theorem is proved in which sufficient conditions for the uniform asymptotic stability of such a system are formulated. Conclusions: the method of vector Lyapunov functions extends to the class of singularly perturbed systems of differential equations with a small factor in the right-hand sides, which are not completely known, but only satisfy certain constraints.

scholarly journals Oriented manifold-based error tracking control for nonholonomic wheeled autonomous vehicles on Lie group for curvilinear approach

2021 ◽  
Vol 3 (6) ◽  
pp. 3608-3626
Author(s):  
Penã Fernández
Keyword(s):  
Autonomous Vehicles ◽  
Tracking Control ◽  
Dynamic Control ◽  
Invariant Subspaces ◽  
Perturbation Approach ◽  
Oriented Manifold ◽  
Trajectory Tracking Control ◽  
Kinematic Constraints ◽  
Control Scheme ◽  
Small Factor

This paper considers the trajectory tracking control of wheeled autonomous vehicles (WAV) with slipping in the wheels, i.e., when the kinematic constraints are not satisfied. Usually, the coordinates system used to represent all control problems suggest invariant subspaces mutually orthogonal, but this  approach can not be enough to treat curvatures significative large at different navigation speed. In order to get a slight im- provement on this topic, there are previous works showing that the kinematic problem (commonly associated with an outer loop) can be resynthesized by using other invariant subspaces, i.e., another representation of the configuration space. For this reason, the proposal reported here uses an oriented-manifold parametrized by a coordinate system on a curve viewpoint of the trajectory to describe the kinematic problem, however, the dynamic control law remains faithful to the singular perturbation approach with invariant subspaces mutually orthogonal, thus, it is possible to include the flexibility through a small factor in the dynamic model (well-known as ε), responsible to avoid the good-performance of the kinematic constraints. Only a common curvature-transformation between orthogonal and curve coordinates will be used to couple both approaches. Finally, it will be observed that when the controller is applied to the control scheme the behavior of the tracking is meaningfully improved.

scholarly journals Do Student Mindsets Differ by Socioeconomic Status and Explain Disparities in Academic Achievement in the United States?

AERA Open ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 233285841985770 ◽  
Author(s):  
Mesmin Destin ◽  
Paul Hanselman ◽  
Jenny Buontempo ◽  
Elizabeth Tipton ◽  
David S. Yeager
Keyword(s):  
Academic Achievement ◽  
Socioeconomic Status ◽  
Public Schools ◽  
The United States ◽  
Negative Association ◽  
Academic Ability ◽  
Socioeconomic Achievement ◽  
Nationally Representative ◽  
Small Factor ◽  
Ninth Grade Students

Students from higher–socioeconomic status (SES) backgrounds show a persistent advantage in academic outcomes over lower-SES students. It is possible that students’ beliefs about academic ability, or mindsets, play some role in contributing to these disparities. Data from a recent nationally representative sample of ninth-grade students in U.S. public schools provided evidence that higher SES was associated with fewer fixed beliefs about academic ability (a group difference of .22 standard deviations). Also, there was a negative association between a fixed mindset and grades that was similar regardless of a student’s SES. Finally, student mindsets were a significant but small factor in explaining the existing relationship between SES and achievement. Altogether, mindsets appear to be associated with socioeconomic circumstances and academic achievement; however, the vast majority of the existing socioeconomic achievement gap in the U.S. is likely driven by the root causes of inequality.

Solar Limb Darkening Color Imaging of the Sun with the Extreme Brightness Capability CAOS Camera

2020 ◽  
Vol 2020 (1) ◽  
pp. 69-73
Author(s):  
Nabeel A. Riza ◽  
Mohsin A. Mazhar ◽  
Nazim Ashraf
Keyword(s):  
Image Data ◽  
Solar Limb ◽  
Integration Time ◽  
The Sun ◽  
Cmos Camera ◽  
Full Spectrum ◽  
Optical Attenuation ◽  
Cmos Sensor ◽  
Small Factor ◽  
Limb Darkening

Experimentally demonstrated for the first time is Coded Access Optical Sensor (CAOS) camera-based imaging of the Sun. Only by using both the shortest 0.029 ms integration time of the scientific CMOS sensor and a very large factor of 10,000 optical attenuation at the entrance of the CMOS camera, one is able to produce the desired unsaturated image of the Sun. In sharp contrast, a small factor of 3.2 optical attenuation is required over a much smaller single photo-detector zone of the CAOS camera to capture the unsaturated Sun image, including color images obtained using red, green, and blue filters. Image data processing shows that both the CMOS camera and CAOS camera show similar Sun limb darkening measurements consistent with prior-art works. The CAOS camera empowers optically and operationally efficient full spectrum (e. g., 350 nm to 2700 nm) imaging of bright heavenly bodies in space, with the potential for creating impact for solar energy farms, space navigation, space exploration and astronomical science.

A Discussion on recent research in air pollution - The dispersion of pollutants in the free atmosphere by the large scale wind systems

1969 ◽  
Vol 265 (1161) ◽  
pp. 273-294 ◽  
Keyword(s):  
Wind Field ◽  
Large Scale ◽  
Three Dimensional ◽  
Horizontal Wind ◽  
Wind Fields ◽  
Free Atmosphere ◽  
Mean Values ◽  
Level Model ◽  
Small Factor ◽  
Numerical Forecast

The travel and dispersion of pollutants in the free atmosphere m ay be investigated by the direct measurement of the distributions of tracer materials such as water vapour, ozone and radioactive substances. Another method is to study the spread of pollutants from a constant point source or the expansion of large clusters, by using air trajectories found by tracking balloons or estimated from sequences of wind values obtained from synoptic charts. So far these latter techniques have usually only taken horizontal motions into account since the balloons are normally maintained at constant levels and the winds taken from the charts have been assumed to be geostrophic. In principle the effect of large (synoptic) scale vertical motions can be included by using the component wind fields given at the different time steps of a numerical forecast integration to construct suitable three-dimensional trajectories. A pilot study of this type at the 900, 700, 500 and 300 m bar pressure levels (90, 70, 50 and 30kN m ~2) using the results of a 24 h numerical forecast by the Meteorological Office’s 10 level model is described. In the case studied the use of constant level trajectories gave horizontal dispersions (variances of the trajectory end points relative to their centre of gravity) which differed by only small amounts from those due to the three dimensional trajectories. The zonal variances exceeded the meridional variances by a small factor and both were 4 to 6 orders greater than those of the corresponding variances in the vertical. In each case for at least 12 to 18 h they were all roughly proportional to the square of the time after release (the ‘short time’ case). The large scale clusters rapidly distorted at rates which increased with their initial size and also with the deformation components of the wind field. At these scales deformation plays a major role in the apparent dispersion and the mean values of total deformation so obtained agreed satisfactorily with those calculated from a kinematic analysis of the horizontal wind field.

Colombian Reactions to the Independence of Panama, 1903-1904

1976 ◽  
Vol 33 (1) ◽  
pp. 130-148
Author(s):  
Joseph L. Arbena
Keyword(s):  
United States ◽  
Political Leadership ◽  
The United States ◽  
Presidential Campaign ◽  
Diplomatic Relations ◽  
Small Factor ◽  
Separatist Movement

Although several Colombians of varying prominence had suggested the possibility of an imminent Isthmian revolt, it seems that the events of and immediately after November 3, 1903, took most of their countrymen by surprise. Certainly there is no evidence of significant prior planning for such a contingency. The achievement of Panamanian independence was followed, in turn, by a Colombian failure to establish a consistent and coherent policy designed either to regain the lost province or to implement terms by which the loss could be made more acceptable. This is not to say that Colombians, officially and unofficially, did nothing in response to the Panamanian separatist movement. Yet what is impressive is not what happened, but what did not happen: There was no sustained military movement against the Isthmus, no break in diplomatic relations with the United States, no serious reprisals against Americans and Isthmians, or their property, in Colombia, and no vigorous protest against the incumbent Colombian political leadership. Panama was apparently not a major issue even during the Presidential campaign and election of 1904. The lack of preparation alluded to above was surely a factor in determining this limited response, but it was a small factor and offers, at best, an incomplete explanation. In fact, the mildness of the Colombian reaction was the product of the unique interaction of domestic and international, contemporary and historical conditions which this article seeks to illuminate.

Nonlinear initial value problems with a singular perturbation of hyperbolic type

1981 ◽  
Vol 89 (3-4) ◽  
pp. 333-345 ◽  
Author(s):  
R. Geel
Keyword(s):  
Initial Value Problems ◽  
A Priori ◽  
Second Order ◽  
Initial Value ◽  
Existence Of A Solution ◽  
Nonlinear Operators ◽  
First Order ◽  
Order Part ◽  
The Difference ◽  
Small Factor

SynopsisThis paper deals with initial value problems in ℝ2 which are governed by a hyperbolic differential equation consisting of a nonlinear first order part and a linear second order part. The second order part of the differential operator contains a small factor ε and can therefore be considered as a perturbation of the nonlinear first order part of the operator.The existence of a solution u together with pointwise a priori estimates for this solution are established by applying a fixed point theorem for nonlinear operators in a Banach space.It is shown that the difference between the solution u and the solution w of the unperturbed nonlinear initial value problem (which follows from the original problem by putting ε = 0) is of order ε, uniformly in compact subsets of ℝ2 where w is sufficiently smooth.

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