Singular Ones Research Articles

On a strong-singular fractional differential equation

It is important we try to solve complicate differential equations specially strong singular ones. We investigate the existence of solutions for a strong-singular fractional boundary value problem under some conditions. In this way, we provide a new technique for our study. We provide an example to illustrate our main result.

It can be us or you. The desubjectification of viewpoint through person choice in Spanish oral and written media discourse

The deictic anchoring of discourse through grammatical persons and their contextual referential scopes is among the most basic resources for clause-level viewpoint establishment. This paper presents an analysis of person choice as a viewpoint-desubjectifying strategy in a corpus of Peninsular Spanish media texts. Two grammatical choices, namely audience-inclusive plural first persons and speaker-inclusive singular second ones, are analyzed and compared regarding both their normalized frequencies across oral and written media genres and the specific discursive contexts where they tend to appear. It is shown that the quantitative and qualitative sides of person choice are closely linked, patterns of genre variation being indexical of different ways of viewpoint construction in context. The plural first person, blending the speaker's viewpoint with that of the audience, highlights interpersonal involvement and is characteristic of genres and contexts where sharedness is a prominent pragmatic value. In turn, the singular second person co-occurs with speakers' personal stances and experiences that are desubjectified through viewpoint displacement from the speaker towards the audience. Furthermore, the strong association of the latter choice with conversational discourse suggests the need to nuance the frequent straightforward identification of orality with subjectivity and that of literacy with objectivity.

Receptive number morphosyntax in children with Down syndrome

ABSTRACTThis study investigated the comprehension of plural morphosyntactic markers and its relationship with numerical comparison abilities in children with Down syndrome (DS). It evaluated 16 Spanish-speaking children with DS (mean verbal mental age = 3;6) and 16 typically developing children with similar receptive vocabulary (mean chronological age = 3;5). Children participated in two preferential looking tasks assessing their abilities to map singular and plural markers to their visual referents and to distinguish one object from more than one. Results showed that both groups of children correctly mapped plural markers to their referents but failed to map singular ones. Furthermore, results also indicated that both groups also looked at collections of more than one object with four objects but not at those with two. The eye movement patterns of children who looked at collections of more than one object suggest a counting-like strategy. These results indicate that comprehension of plural markers of children with DS is similar to that of their typically developing peers; however, it is not related to their numerical abilities.

Dark, singular and straddled optical solitons in birefringent fibers with generalized anti–cubic nonlinearity

This paper enumerates optical soliton solutions in birefringent fibers having generalized form of anti–cubic law of refractive index. The unified Riccati equation expansion yields dark, singular as well as solitons that are straddled between dark and singular ones. A few additional solutions emerge from the integration scheme as a byproduct.

Singular radial solutions for the Keller-Segel equation in high dimension

We study singular radially symmetric solution of the stationary Keller-Segel equation, that is, an elliptic equation with exponential nonlinearity, which is super-critical in dimension N≥3. The solutions are unbounded at the origin and we show that they describe the asymptotics of bifurcation branches of regular solutions. It is shown that for any ball and any k≥0, there is a singular solution that satisfies Neumann boundary condition and oscillates at least k times around the constant equilibrium. Moreover, we prove that in dimension 3≤N≤9 there are regular solutions satisfying Neumann boundary conditions that are close to singular ones when the value at the origin is close to infinity. Hence, it follows that there exist regular solutions on any ball with arbitrarily fast oscillations. For generic radii, we show that the bifurcation branches of regular solutions oscillate in the bifurcation plane when 4≤N≤9 and approach to a singular solution. In dimension N>10, we show that the Morse index of the singular solution is finite, and therefore the existence of regular solutions with fast oscillations is not expected.

Thermal 3D model for non-homogeneous elements in mobile devices

A mathematical model for the analysis of heat exchange between the environment and an isotropic space layer with an alien inclusions is developed, which is heated by a heat flux centered on one of the boundary surfaces. For this purpose, using the theory of generalized functions, the coefficient of thermal conductivity of this structure is depicted as one unit for the whole system. In view of this, instead of two equations of thermal conductivity for the layer and the inclusion and conditions of perfect thermal contact on the surfaces of the junction between them, one equation of thermal conductivity was obtained in the generalized derivatives with breaking coefficients. We consider the case when the inclusion sizes are small compared to the distances from the inclusion surfaces to the boundary surfaces of the layer. In this connection, the combined thermophysical parameters were introduced and the thermal coefficients of the thermal conductivity equation were transformed into singular ones. For the solution of the boundary value problem of thermal conductivity containing this equation and boundary conditions on the boundary surfaces of the layer, an integral Fourier transform was used and, as a result, an analytical solution of the problem in the images was obtained. The inverse integral Fourier transform was applied to this solution, which made it possible to obtain the final analytical solution of the original problem. The analytical solution obtained is presented as a non-native double convergent integral. To determine the numerical values ​​of the temperature in the above design, as well as to analyze the heat exchange between the layer and the environment caused by different temperature regimes due to the heating of the inhomogeneous layer by a heat source concentrated in the area of ​​inclusion, computational programs have been developed. Using these programs, graphs are displayed showing the behavior of curves constructed using numerical values ​​of the temperature distribution depending on the spatial coordinates for different inclusion materials. The obtained numerical values ​​of temperature indicate a significant influence of the inclusion on its distribution in the design "layer-inclusion". The software also makes it possible to analyze these inhomogeneous media with respect to their heat resistance during heating. As a consequence, it becomes possible to raise and protect it from overheating, which can cause destruction not only of individual elements, but also of the whole structure.

K-stability of cubic threefolds

We prove the K-moduli space of cubic threefolds is identical to their GIT moduli. More precisely, the K-(semi,poly)-stability of cubic threefolds coincide to the corresponding GIT stabilities, which could be explicitly calculated. In particular, this implies that all smooth cubic threefolds admit K\"ahler-Einstein metric as well as provides a precise list of singular KE ones. To achieve this, our main new contribution is an estimate in dimension three of the volumes of kawamata log terminal singularities introduced by Chi Li. This is obtained via a detailed study of the classification of three dimensional canonical and terminal singularities, which was established during the study of the explicit three dimensional minimal model program.

On Euler preconditioned SHSS iterative method for a class of complex symmetric linear systems

In this paper, we propose an Euler preconditioned single-step HSS (EP-SHSS) iterative method for solving a broad class of complex symmetric linear systems. The proposed method can be applied not only to the non-singular complex symmetric linear systems but also to the singular ones. The convergence (semi-convergence) properties of the proposed method are carefully discussed under suitable restrictions. Furthermore, we consider the acceleration of the EP-SHSS method by preconditioned Krylov subspace method and discuss the spectral properties of the corresponding preconditioned matrix. Numerical experiments verify the effectiveness of the EP-SHSS method either as a solver or as a preconditioner for solving both non-singular and singular complex symmetric linear systems.

Total Least Squares Spline Approximation

Spline approximation, using both values y i and x i as observations, is of vital importance for engineering geodesy, e.g., for approximation of profiles measured with terrestrial laser scanners, because it enables the consideration of arbitrary dispersion matrices for the observations. In the special case of equally weighted and uncorrelated observations, the resulting error vectors are orthogonal to the graph of the spline function and hence can be utilized for deformation monitoring purposes. Based on a functional model that uses cubic polynomials and constraints for continuity, smoothness and continuous curvature, the case of spline approximation with both the values y i and x i as observations is considered. In this case, some of the columns of the functional matrix contain observations and are thus subject to random errors. In the literature on mathematics and statistics this case is known as an errors-in-variables (EIV) model for which a so-called “total least squares” (TLS) solution can be computed. If weights for the observations and additional constraints for the unknowns are introduced, a “constrained weighted total least squares” (CWTLS) problem is obtained. In this contribution, it is shown that the solution for this problem can be obtained from a rigorous solution of an iteratively linearized Gauss-Helmert (GH) model. The advantage of this model is that it does not impose any restrictions on the form of the functional relationship between the involved quantities. Furthermore, dispersion matrices can be introduced without limitations, even the consideration of singular ones is possible. Therefore, the iteratively linearized GH model can be regarded as a generalized approach for solving CWTLS problems. Using a numerical example it is demonstrated how the GH model can be applied to obtain a spline approximation with orthogonal error vectors. The error vectors are compared with those derived from two least squares (LS) approaches.

Being a Participant Matters: Event-Related Potentials Show That Markedness Modulates Person Agreement in Spanish.

The present study uses event-related potentials to examine subject–verb person agreement in Spanish, with a focus on how markedness with respect to the speech participant status of the subject modulates processing. Morphological theory proposes a markedness distinction between first and second person, on the one hand, and third person on the other. The claim is that both the first and second persons are participants in the speech act, since they play the speaker and addressee roles, respectively. In contrast, third person refers to whomever is neither the speaker nor the addressee (i.e., it is unmarked for person). We manipulated speech participant by probing person agreement with both first-person singular subjects (e.g., yo…lloro “I…cry-1ST PERSON-SG”) and third-person singular ones (e.g., la viuda…llora “the widow…cry-3RD PERSON-SG”). We also manipulated agreement by crossing first-person singular subjects with third-person singular verbs (e.g., yo…∗llora “I…cry-3RD PERSON-SG”) and vice versa (e.g., la viuda…∗lloro “the widow…cry-1ST PERSON-SG”). Results from 28 native speakers of Spanish revealed robust positivities for both types of person violations, relative to their grammatical counterparts between 500 and 1000 ms, an effect that shows a central-posterior distribution, with a right hemisphere bias. This positivity is consistent with the P600, a component associated with a number of morphosyntactic operations (and reanalysis processes more generally). No negativities emerged before the P600 (between 250 and 450 ms), although both error types yielded an anterior negativity in the P600 time window, an effect that has been argued to reflect the memory costs associated with keeping the errors in working memory to provide a sentence-final judgment. Crucially, person violations with a marked subject (e.g., yo…∗llora “I…cry-3RD PERSON-SG”) yielded a larger P600 than the opposite error type between 700 and 900 ms. This effect is consistent with the possibility that, upon encountering a subject with marked features, feature activation allows the parser to generate a stronger prediction regarding the upcoming verb. The larger P600 for person violations with a marked subject might index the reanalysis process that the parser initiates when there is a conflict between a highly expected verbal form (i.e., more so than in the conditions with an unmarked subject) and the form that is actually encountered.

Linear Structures of Correlation Function of Odd-Length Generalized Binary Barker Sequences

Spread-spectrum, wideband and pulse compression are well-known currently in use technologies for radar, telecommunication, navigation and other radio systems. The main theoretical problem concerning these technologies boils down to a synthesis and study of signals with certain correlation properties. A collection of mathematical models, which are generation rules for binary sequences, and related sequences with regular structures, which generalize structural features of known binary Barker sequences, were suggested and described in literature and may be taken as a kind of generalized binary Barker sequences. In contrast with known binary Barker sequences, which are known up to length N = 13 and widely used in radar and other radio systems and techniques, the generalized binary Barker sequences can be synthesized by means of deterministic generation rules for lengths N = 4 k –1, N = 4 k , N = 4 k +1, where k is a positive integer, and contain binary Barker sequences of lengths N = 3, 4, 5, 7, 11, 13 as a particular case. However, generally, the correlation function of generalized binary Barker sequence has a high value of sidelobes and therefore they cannot be used separately for high quality signal detection. Because of that, multiplicative complementary sets of generalized binary Barker sequences with a mutual sidelobe reduction are usable, similarly to Golay additive complementary sequences. It is shown that a structuring of the correlation function of odd-length generalized binary Barker sequences lies in the fact that the correlation function may be presented by some finite number of linear structures and singular ones, which are exceptional points of the correlation function. It has been determined that the number of such structures for any odd-length generalized binary Barker sequence does not exceed 7 pieces, of which no more than 3 pieces are linear structures, and no more than 4 pieces are exceptional points of the correlation function. On the basis of the structural analysis a complete system of analytical expressions, which based on above-mentioned linear and singular structures, for the correlation function of off-length generalized binary Barker sequence of any type and subtype is synthesized and presented. Examples of a structuring of the correlation function, which based on linear and singular structures, for odd-length generalized binary Barker sequences of different types and subtypes at k = 8 (lengths N = 31 and N = 33) are done. The theoretical significance of presented results lies in the obtaining of a new additional feature of “generalization” of generalized binary Barker sequences, namely, the structuring of their correlation functions based on linear structures. The obtained results make possible a description of signal components, which are based on odd-length generalized binary Barker sequences, after their matched filtering by means of linear constituents. Bibl. 10, Fig. 3, Tables 3.

A Modified Spectral PRP Conjugate Gradient Projection Method for Solving Large‐Scale Monotone Equations and Its Application in Compressed Sensing

In this paper, we develop an algorithm to solve nonlinear system of monotone equations, which is a combination of a modified spectral PRP (Polak‐Ribière‐Polyak) conjugate gradient method and a projection method. The search direction in this algorithm is proved to be sufficiently descent for any line search rule. A line search strategy in the literature is modified such that a better step length is more easily obtained without the difficulty of choosing an appropriate weight in the original one. Global convergence of the algorithm is proved under mild assumptions. Numerical tests and preliminary application in recovering sparse signals indicate that the developed algorithm outperforms the state‐of‐the‐art similar algorithms available in the literature, especially for solving large‐scale problems and singular ones.

Organizational creativity as idea work: Intertextual placing and legitimating imaginings in media development and oil exploration

How do we understand the nature of organizational creativity when dealing with complex, composite ideas rather than singular ones? In response to this question, we problematize assumptions of the linearity of creative processes and the singularity of ideas in mainstream creativity theory. We draw on the work of Bakhtin and longitudinal research in two contrasting cases: developing hydrocarbon prospects and concepts for films and TV series. From these two cases, we highlight two forms of work on ideas: (i) intertextual placing, whereby focal ideas are constituted by being connected to other elements in a larger idea field; and (ii) legitimating imaginings, where ideas of what to do are linked to ideas of what is worth doing and becoming. This ongoing constitution and legitimating is not confined to particular stages but takes place in practices of generating, connecting, communicating, evaluating and reshaping ideas, which we call idea work. The article contributes to a better understanding of the processual character of creativity and the deeply intertextual nature of ideas, including the multiplicity of idea content and shifting parts–whole relationships. Idea work also serves to explore the neglected role of co-optative power in creativity.

On the number and complete continuity of weighted eigenvalues of measure differential equations

The classical eigenvalue theory for second-order ordinary differential equations (ODE) describes the spatial oscillation of strings whose distributions of masses are absolutely continuous. For general distributions of masses, including completely singular ones, the spatial oscillation can be explained using measure differential equations (MDE). In this paper we will study weighted eigenvalue problems for second-order MDE with general distributions or measures. It will be shown that the numbers of weighted eigenvalues depend on measures and may be finite. Furthermore, it will be proved that weighted eigenvalues and eigenfunctions are completely continuous in measures, i.e., when measures are convergent in the weak$^*$ topology, these eigen-pairs are strongly convergent. The present paper and the work of Meng and Zhang (Dependence of solutions and eigenvalues of measure differential equations on measures, J. Differential Equations, 254 (2013), 2196-2232, have given an extension of the classical Sturm-Liouville theory to the measure version of ODE.

Infinite soft theorems from gauge symmetry

In this letter we show that the soft behaviour of photons and graviton amplitudes, after projection, can be determined to infinite order in soft expansion via ordinary on-shell gauge invariance. In particular, as one of the particle's momenta becomes soft, gauge invariance relates the non-singular diagrams of an n-point amplitude to that of the singular ones up to possible homogeneous terms. We demonstrate that with a particular projection of the soft-limit, the homogeneous terms do not contribute, and one arrives at an infinite soft theorem. This reproduces the result recently derived from the Ward identity of large gauge transformations. We also discuss the modification of these soft theorems due to the presence of higher-dimensional operators.

Microfluidic Devices for Drug Assays.

In this review, we give an overview of the current state of microfluidic-based high-throughput drug assays. In this highly interdisciplinary research field, various approaches have been applied to high-throughput drug screening, including microtiter plate, droplets microfluidics as well as continuous flow, diffusion and concentration gradients-based microfluidic drug assays. Therefore, we reviewed over 100 recent publications in the field and sorted them according to their microfluidic approach. As a result, we are showcasing, comparing and discussing broadly applied approaches as well as singular promising ones that might contribute to shaping the future of this field.

Exact solutions and singularities of an X-point collapse in Hall magnetohydrodynamics

Magnetic collapse is a basic dynamic scenario forming a current sheet, where magnetic reconnection can take place and convert magnetic energy into other forms. We discuss a self-similar magnetic collapse of a planar X-point configuration in incompressible Hall magnetohydrodynamics. There are two classes of exact solutions: globally regular and singular ones. The structure of solutions provides an exact expression for the time of breakdown in terms of the initial conditions.

Accurate and Efficient Singularity Treatment in Integral Equation Discontinuous Galerkin Method

A novel approach based on the singularity cancellation (SC) is proposed to accurately and efficiently evaluate the singular integrals arising in the integral equation discontinuous Galerkin (IEDG) method. Since IEDG employs the half-RWG basis function to discretize the 3-D integral equations, the operation of using Green’s identity to convert the strongly singular integrals into the weakly singular ones gives rise to 3-D integrals along with 4-D integrals. Thus, the well-developed SC methods based on Duffy’s transformation for the 4-D integrals arising in the traditional Galerkin method cannot be directly applied to IEDG. To solve this problem, a new scheme is developed to cancel out the singularities of the 3-D integrals in IEDG. The accuracy and efficiency of the proposed method are validated and demonstrated by several numerical results.

Tree crowns grow into self-similar shapes controlled by gravity and light sensing.

Plants have developed different tropisms: in particular, they reorient the growth of their branches towards the light (phototropism) or upwards (gravitropism). How these tropisms affect the shape of a tree crown remains unanswered. We address this question by developing a propagating front model of tree growth. Being length-free, this model leads to self-similar solutions after a long period of time, which are independent of the initial conditions. Varying the intensities of each tropism, different self-similar shapes emerge, including singular ones. Interestingly, these shapes bear similarities to existing tree species. It is concluded that the core of specific crown shapes in trees relies on the balance between tropisms.

THEY AND ITS LEMMAS AS NON-BINARY THIRD PERSON SINGULAR PRONOUNS IN THE WASHINGTON POST

In recent years, it is found that pronoun they and its lemmas are used to refer to singular person to show that the person does not wish to be identified as one of gender binaries. This phenomenon occurs in The Washington Post having added singular they to their stylebook. Therefore this paper aims at elaborating how pronouns they, them, their, theirs, and themselves are used as singular ones in the articles of The Washington Post published in 2016. With the aid of corpus instrument software, this study qualitatively analyses a small corpus consisting of 100 articles. References of pronouns identified as singular are proceeded as the data source of this study and categorized into Crystal’s (2003) main classes of noun and Cobuild’s (2011) classification of indefinite pronoun. The study reveals that The Washington Post used they as singular with the references of proper noun which consists of names of people and organizations, common count concrete noun which consists of nouns denoting persons and a noun denoting things, common count abstract noun consisting of nouns denoting abstract entities, and 6 indefinite pronouns which are used to refer to persons. These references are found mostly to be non-referential, where gender is indefinite. However, some are found to be referential which are common count concrete noun child and proper nouns in the form of names of people. These references refer to individuals who identify themselves not in one of gender binaries, instead they are found to be used in a context regarding LGBT.