Degenerate Form Research Articles

Flat centroaffine surfaces with the degenerate second fundamental form and vanishing Pick invariant in [formula omitted

In this paper, we get the centroaffine theorema egregium of centroaffine immersions with codimension two. Then by solving certain partial differential equations, we obtain some classification results for flat centroaffine surfaces in R4, under the condition of degenerate second fundamental form and vanishing Pick invariant. Finally, some examples with respect to the classification results are discussed.

One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity

One-dimensional solute transport, originating from a continuous uniform point source, is studied along unsteady longitudinal flow through a heterogeneous medium of semi-infinite extent. Velocity is considered as directly proportional to the linear spatially-dependent function that defines the heterogeneity. It is also assumed temporally dependent. It is expressed in both the independent variables in degenerate form. The dispersion parameter is considered to be proportional to square of the velocity. Certain new independent variables are introduced through separate transformations to reduce the variable coefficients of the advection–diffusion equation to constant coefficients. The Laplace Transformation Technique (LTT) is used to obtain the desired solution. The effects of heterogeneity and unsteadiness on the solute transport are investigated. Editor D. Koutsoyiannis; Associate editor F.F. Hattermann Citation Kumar, A., Jaiswal, D.K., and Kumar, N., 2012. One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity. Hydrological Sciences Journal, 57 (6), 1223–1230.

Experimental Evidence for Metallurgical Modification Associated to Chunky Graphite in Heavy-Section Ductile Iron Castings

Heavy-section castings made of spheroidal graphite cast irons are known to be prone to graphite degeneracy. Upon the various degenerate forms of graphite reported in the literature, chunky graphite is the most common and detrimental one. A great deal of effort has been made for many years to prevent its formation but no convincing description of the factors controlling its appearance has been given so far.

Optimal harvesting and planting control in stochastic logistic population models

We consider the optimal harvesting and planting control problem to maximize the expected total net benefits in the stochastic logistic population model. The variational inequality associated with this problem is given by the degenerate form of elliptic type with quadratic coefficients. Using the viscosity solutions technique, we solve the corresponding penalty equation and show the existence of a solution to the variational inequality. The optimal harvesting and planting policy is characterized in terms of two thresholds for the variational inequality.

One-Dimensional Pollutant’s Advective-Diffusive Transport from a Varying Pulse-Type Point Source through a Medium of Linear Heterogeneity

AbstractAnalytical solutions of one-dimensional (1D) advection-diffusion equations (ADE) are obtained subject to an initially pollutant-free domain and varying pulse-type input conditions. The medium is considered heterogeneous and of semi-infinite extent. The heterogeneity is defined by considering the velocity as a spatially dependent, linear, non homogeneous increasing function. It is interpolated in a finite domain in which concentration values are to be evaluated. The unsteadiness of the exponential form of velocity and dispersivity is also considered. The expression for velocity is written in degenerate form. Analytical solutions are obtained when dispersivity depends upon the velocity. The Laplace integral transform technique (LITT) has been used.

The Culture of Japanese Fascism (review)

Reviewed by: The Culture of Japanese Fascism Bill Mihalopoulos The Culture of Japanese Fascism. Edited by Alan Tansman. Durham, N.C.: Duke University Press, 2009. 496 pp. $99.95 (cloth); $27.95 (paper). The Culture of Japanese Fascism is a multidisciplinary collection of essays dealing with the relation between aesthetics—as a critique of experience and "the true situation of the present"—and political action. The common thread among the diverse collection of essays is the starting point of analysis: Japan's fascist turn was a product of efforts to come to terms with "modernity." Japanese intellectuals experienced the shock of rapid change as a fundamental homesickness for a past when the world was fully accessible, and the transparency in human relations safeguarded Japanese civilization from outside corruption. In an effort to overturn the forces of modernity responsible for the present-day corruption and degenerate forms of life, Japanese thinkers, rural leaders, and social reformers turned to culture and community as a solution. Culture and tradition were conceptualized as the storehouses of an unchanging, transhistorical Japanese essence. In terms of aesthetics, culture and tradition were the elixir to prevent Japan turning into an inferior copy of the West. Politically, culture and the tradition held the key for Japan's quest to liberate Asia from Western colonial hegemony. More or less, each essay deals with a core issue in Japan's fascistic turn: how to revert to the premodern unity of ethics, politics, and economics. Capitalist development brought a rupture from the past. Precapitalist Japan was organized around direct interpersonal relations. Capitalism (re)organizes society impersonally, by means of the market, transforming labor power into production power. Capitalist modernity also undermined existing bonds of solidarity. Politics and economics no longer constituted a coherent whole. The intensification and spread of commodity relations from the mid 1900s transformed the outer and inner life of Japanese society. After the Russo-Japanese war, the Japanese economy shifted from state-sponsored projects aimed at beefing up military and technological infrastructure to commodity production. The transformation to a higher level of capitalist production brought [End Page 893] about a significant transformation in social agency, as the wealth of objects and the knowledge and aspirations that constituted the lived world became subsumed under the capitalist principle of money begetting more money. The multiple new forms of life unleashed by the forces of commodity production transformed simultaneously the mind and material world: human social relations were objectified into things, and consciousness (the realm of judgment and value) was subjected to the principles of rationalization that constitute the world of commodities. That is to say, capitalist development involved the concurrent transformations in relations of production and subjectivity. This transformation led to a crisis of government. Namely, Japanese leaders had to invent new ways of governing to coordinate a whole field of new realities and multiplication of interests that threatened to tear Japan apart. What each essay reveals is a snapshot of how Japan's fascist turn is the gradual evolvement of heterogeneous forms of government, often conflicting, that intervened deep in everyday life, aiming to constitute a uniformed subjectivity. The vapor-like quality of fascism was due to the micro-level alignments of everyday choices and personal investments to the power circuits of the state. The Culture of Japanese Fascism is enriched by a tension between three distinct strands in analyzing fascism. Kevin Doak, Aaron Gerow, Noriko Aso, and Aaron Skabelund attempt to situate fascist ideals as a cultural manifestation of ethnic ultranationalism. Harry Harootunian, Michael Baskett, and Angus Lockyer are more interested in fascist aesthetics as a transnational movement where Japan's turn to ethical and cultural exceptionalism is an effect of capitalism. This approach posits an important point of debate that needs clarification. In this approach, fascism does not refer to the state fascism of Mussolini but to a generic authoritarian propensity immanent in capitalist societies. This propensity, or force, comes to the fore in times of crisis. During times of danger, diverse institutions in capitalist societies, such as school, family, police, and religious institutions become despotic and limit individual and collective action by demanding that one and sundry act and behave like "responsible" citizens, or, in the...

Tree-structured algorithm for long weak motif discovery

Motifs in DNA sequences often appear in degenerate form, so there has been an increased interest in computational algorithms for weak motif discovery. Probabilistic algorithms are unable to detect weak motifs while exact methods have been able to detect only short weak motifs. This article proposes an exact tree-based motif detection (TreeMotif) algorithm capable of discovering longer and weaker motifs than by the existing methods. TreeMotif converts the graphical representation of motifs into a tree-structured representation in which a tree that branches with nodes from every sequence represents motif instances. The method of tree construction is novel to motif discovery based on graphical representation. TreeMotif is more efficient and scalable in handling longer and weaker motifs than the existing algorithms in terms of accuracy and execution time. The performances of TreeMotif were demonstrated on synthetic data as well as on real biological data. https://sites.google.com/site/shqssw/treemotif sunh0013@e.ntu.edu.sg Supplementary data are available at Bioinformatics online.

Families of curve congruences on Lorentzian surfaces and pencils of quadratic forms

We define and study families of conjugate and reflected curve congruences associated to a self-adjoint operator on a smooth and oriented surface M endowed with a Lorentzian metric g. These families trace parts of the pencil joining the equations of the -asymptotic and the -principal curves, and the pencil joining the -characteristic and the -principal curves, respectively. The binary differential equations (BDEs) of these curves can be viewed as points in the projective plane. Using the polar lines of various BDEs with respect to the conic of degenerate quadratic forms, we obtain geometric results on the above pencils and their relation with the metric g, on the type of solutions of a given BDE, of its -conjugate equation and on BDEs with orthogonal roots.

Forms of higher degree permitting composition

Two new constructions for cubic forms permitting composition of rank 3 are given. Classes of highly degenerate cubic forms N over fields which permit composition are constructed out of forms permitting composition over projective spaces. As a preparation, we study nondegenerate cubic forms which permit composition over certain rings and locally ringed spaces.

One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

The one-dimensional linear advection–diffusion equation is solved analytically by using the Laplace integral transform. The solute transport as well as the flow field is considered to be unsteady, both of independent patterns. The solute dispersion occurs through an inhomogeneous semi-infinite medium. Hence, velocity is considered to be an increasing function of the space variable, linearly interpolated in a finite domain in which solute dispersion behaviour is studied. Dispersion is considered to be proportional to the square of the spatial linear function. Thus, the coefficients of the advection–diffusion equation are functions of both the independent variables, but the expression for each coefficient is considered in degenerate form. These coefficients are reduced into constant coefficients with the help of a new space variable, introduced in our earlier works, and new time variables. The source of the solute is considered to be a stationary uniform point source of pulse type.

Horizontal solute transport from a pulse type source along temporally and spatially dependent flow: Analytical solution

Summary Transport of solute mass transport, originating from a uniform pulse-type stationary point source through a heterogeneous semi-infinite horizontal medium, is studied. The heterogeneity is described by position dependent linear non-homogeneous expression for the velocity. The exponential unsteady variation in velocity of decreasing/increasing is also considered. The variation in dispersion parameter due to heterogeneity is considered proportional to square of that in the velocity. But the same due to unsteadiness is proportional to a power of the velocity which may take any value between 1 and 2 or outside this range. The variable coefficients of the two-dimensional advection–diffusion equation are put in degenerate form. These are reduced into constant coefficients with the help of new independent variables introduced at different stages, paving the way for using Laplace transformation technique to get the desired solution.

From discrete Painlevé equations to mappings with periodic coefficients and back

We investigate relations between two families of discrete Painlevé equations obtained respectively from degenerate forms of q-PIII and q-PVI. Our approach is based on the recently derived extensions of QRT mappings to ones with periodic coefficients. We establish the relationships that exist between the two families by deautonomizing the corresponding mappings with periodic coefficients. In the process we obtain mappings that cannot be extended to q-Painlevé forms and show that these mappings are not of infinite order.

On the role of revenue-sharing contracts in supply chains

The supply chain coordinating role of revenue-sharing has, to date, been examined only in static models. With downstream competition, the central conclusion in these models is negative: revenue-sharing cannot, except in degenerate form, achieve coordination. Incorporating dynamics, by allowing inventory carryover in discrete time, this paper establishes a foundation for revenue-sharing contracts in aligning incentives.

False constraints. A toy model for studying dynamical systems with degenerate Hessian form

This paper studies various aspects of the motion of relativistic rotators, both in the presence and absence of external fields, using a toy model which, in a sense, can be regarded as a non-relativistic limit of the rotators. In a simpler setup, this enables one to gain an insight into the principal difference between mechanical systems with singular and non-singular Hessian, whilst avoiding the complications resulting from the more intricate form of the equations of motion in the fully relativistic regime. In particular, one can comprehend the apparent contradiction between Hessian singularity and simultaneous occurrence of unique solutions for the motion of the fundamental relativistic rotator minimally coupled to the electromagnetic field. With the aid of the toy model the author supports and illustrates his thesis put forward elsewhere that the Hessian singularity is a defect that makes physically unviable some geometric models of spinning particles considered in the literature.

Free Vibration Analysis of a Circular Plate With Multiple Circular Holes by Using Indirect BIEM and Addition Theorem

In this paper, natural frequencies and natural modes of a circular plate with multiple circular holes are theoretically derived and numerically determined by using the indirect boundary integral formulation, the addition theorem, and the complex Fourier series. Owing to the addition theorem, all kernel functions are expanded into degenerate forms and further expressed in the same polar coordinates centered at one circle where the boundary conditions are specified. Not only the computation of the principal value is avoided but also the calculation of higher-order derivatives can be easily determined. By matching boundary conditions, a coupled infinite system of linear algebraic equations is derived as an analytical model for the free vibration of a circular plate with multiple circular holes. The direct-searching approach is utilized in the truncated finite system to determine the natural frequency through singular value decomposition. After determining the unknown Fourier coefficients, the corresponding mode shapes are obtained by using the indirect boundary integral formulations. Some numerical eigensolutions are presented and then utilized to explain some physical phenomenon such as the beating and the dynamic stress concentration. Good accuracy and fast rate of convergence are the main features of the present method, thanks to the analytical approach.

Characterizations of Bent and Almost Bent Function on $${\mathbb{Z}_p^2}$$

Bent and almost-bent functions on $${\mathbb{Z}_p^2}$$ are studied in this paper. By calculating certain exponential sum and using a technique due to Hou (Finite Fields Appl 10:566–582, 2004), we obtain a degree bound for quasi-bent functions, and prove that almost-bent functions on $${\mathbb{Z}_p^2}$$ are equivalent to a degenerate quadratic form. From the viewpoint of relative difference sets, we also characterize bent functions on $${\mathbb{Z}_p^2}$$ in two classes of $${\mathcal{M}}$$ ’s and $${\mathcal{PS}}$$ ’s, and show that the graph set corresponding to a bent function on $${\mathbb{Z}_p^2}$$ can be written as the sum of a graph set of $${\mathcal{M}}$$ ’s type bent function and another group ring element. By using our characterization and some technique of permutation polynomial, we obtain the result: a bent function must be of $${\mathcal{M}}$$ ’s type if its corresponding set contains more than (p − 3)/2 flats. A problem proposed by Ma and Pott (J Algebra 175:505–525, 1995) is therefore partially answered.

A localization technique for linear preserver problems

We introduce a new general technique for solving linear preserver problems. The idea is to localize a given linear preserver ϕ at each non-zero vector. In such a way we get vector-valued linear maps on the space of matrices which inherit certain properties from ϕ . If we can prove that such induced maps have a standard form, then ϕ itself has either a standard form or a very special degenerate form. We apply this technique to characterize linear preservers of full rank. Using this technique we further reprove two classical results describing the general form of linear preservers of rank one and linear preservers of the unitary (or orthogonal) group.

Eigensolutions of a circular flexural plate with multiple circular holes by using the direct BIEM and addition theorem

The purpose of this paper is to present an analytical formulation to describe the free vibration of a circular flexural plate with multiple circular holes by using the null field integral formulation, the addition theorem and complex Fourier series. Owing to the addition theorem, all kernel functions are represented in the degenerate form and further transformed into the same polar coordinates centered at one of circles, where the boundary conditions are specified. Thus, not only the computation of the principal value for integrals is avoided but also the calculation of higher-order derivatives in the flexural plate problem can be easily determined. By matching the specified boundary conditions, a coupled infinite system of simultaneous linear algebraic equations is derived as an analytical model for the title problem. According to the direct searching approach, natural frequencies are numerically determined through the singular value decomposition (SVD) in the truncated finite system. After determining the unknown Fourier coefficients, the corresponding mode shapes are obtained by using the direct boundary integral formulations for the domain points. Several numerical results are presented. In addition, the inherent problem of spurious eigenvalue using the integral formulation is investigated and the SVD updating technique is adopted to suppress the occurrence of spurious eigenvalues. Excellent accuracy, fast rate of convergence and high computational efficiency are advantages of the present method thanks to its analytical features.

Networked buffering: a basic mechanism for distributed robustness in complex adaptive systems

A generic mechanism - networked buffering - is proposed for the generation of robust traits in complex systems. It requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role within a system and 2) agents are degenerate, i.e. there exists partial overlap in the functional capabilities of agents. Given these prerequisites, degenerate systems can readily produce a distributed systemic response to local perturbations. Reciprocally, excess resources related to a single function can indirectly support multiple unrelated functions within a degenerate system. In models of genome:proteome mappings for which localized decision-making and modularity of genetic functions are assumed, we verify that such distributed compensatory effects cause enhanced robustness of system traits. The conditions needed for networked buffering to occur are neither demanding nor rare, supporting the conjecture that degeneracy may fundamentally underpin distributed robustness within several biotic and abiotic systems. For instance, networked buffering offers new insights into systems engineering and planning activities that occur under high uncertainty. It may also help explain recent developments in understanding the origins of resilience within complex ecosystems.

ChemInform Abstract: Isomerism and Novel Magnetic Order in Mn13 Cluster.

First principles calculations based on the generalized gradient approximation to the density functional theory reveal the existence of two nearly degenerate isomeric forms of Mn13 cluster. The lowest energy structure corresponds to icosahedric packing that lies 0.65 eV lower than a caged structure with a hexagonal close-packed motif. Magnetically, however, these two isomers are very different: while the icosahedric structure is ferrimagnetic with a total magnetic moment of 33 μB, the hexagonal close-packed structure is a de facto antiferromagnet with a magnetic moment of 17 μB. The two isomers also have different ionization potentials, 5.19 and 4.82 eV, in good agreement with experiment.