Fundamental Form Research Articles

Synaptic homeostats: latent plasticity revealed at the Drosophila neuromuscular junction.

Homeostatic signaling systems are fundamental forms of biological regulation that maintain stable functionality in a changing environment. In the nervous system, synapses are crucial substrates for homeostatic modulation, serving to establish, maintain, and modify the balance of excitation and inhibition. Synapses must be sufficiently flexible to enable the plasticity required for learning and memory but also endowed with the stability to last a lifetime. In response to the processes of development, growth, remodeling, aging, and disease that challenge synapses, latent forms of adaptive plasticity become activated to maintain synaptic stability. In recent years, new insights into the homeostatic control of synaptic function have been achieved using the powerful Drosophila neuromuscular junction (NMJ). This review will focus on work over the past 10years that has illuminated the cellular and molecular mechanisms of five homeostats that operate at the fly NMJ. These homeostats adapt to loss of postsynaptic neurotransmitter receptor functionality, glutamate imbalance, axonal injury, as well as aberrant synaptic growth and target innervation. These diverse homeostats work independently yet can be simultaneously expressed to balance neurotransmission. Growing evidence from this model glutamatergic synapse suggests these ancient homeostatic signaling systems emerged early in evolution and are fundamental forms of plasticity that also function to stabilize mammalian cholinergic NMJs and glutamatergic central synapses.

On the geometry of the second fundamental form of the Torelli map

In this paper we give a geometric interpretation of the second fundamental form of the period map of curves and we use it to improve the upper bounds on the dimension of a totally geodesic subvariety Y Y of A g \mathsf {A}_g generically contained in the Torelli locus obtained by Elisabetta Colombo, Paola Frediani, and Alessandro Ghigi [Internat. J. Math. 26 (2015), no. 1, 1550005] and A. Ghigi, P. Pirola, and S. Torelli (to appear on Communications in Contemporary Mathematics, https:// doi.org/10.1142/S0219199720500200). We get dim ⁡ Y ≤ 2 g − 1 \dim Y \leq 2g-1 if g g is even, dim ⁡ Y ≤ 2 g \dim Y \leq 2g if g g is odd. We also study totally geodesic subvarieties Z Z of A g \mathsf {A}_g generically contained in the hyperelliptic Torelli locus and we show that dim ⁡ Z ≤ g + 1 \dim Z \leq g+1 .

Self-Expanders of the Mean Curvature Flow

We study self-expanding solutions M^{m}subset mathbb {R}^{n} of the mean curvature flow. One of our main results is, that complete mean convex self-expanding hypersurfaces are products of self-expanding curves and flat subspaces, if and only if the function |A|2/|H|2 attains a local maximum, where A denotes the second fundamental form and H the mean curvature vector of M. If the principal normal ξ = H/|H| is parallel in the normal bundle, then a similar result holds in higher codimension for the function |Aξ|2/|H|2, where Aξ is the second fundamental form with respect to ξ. As a corollary we obtain that complete mean convex self-expanders attain strictly positive scalar curvature, if they are smoothly asymptotic to cones of non-negative scalar curvature. In particular, in dimension 2 any mean convex self-expander that is asymptotic to a cone must be strictly convex.

Radical Empiricism, Neutral Monism, and the Elements of Mind

AbstractNeutral monism is the view that both ‘mind’ and ‘matter’ are grounded in a more fundamental form of reality that is intrinsically neither mental nor material. It has often been treated as an odd fringe theory deserving of at most a footnote in the broader philosophical debates. Yet such attitudes do a grave disservice to its sophistications and significance for late nineteenth and early twentieth-century philosophy of mind and psychology. This paper sheds light on this neglected view by situating it within broader historical monist debates about the mind and bringing attention to one of its central internal disputes regarding ‘mental chemistry’. By taking a closer look at how Ernst Mach, William James, and Bertrand Russell address the question of whether and how our mental episodes are composed of more basic elements, it highlights deep differences among their conceptions of the fundamental ‘neutral stuff’ and its relations to ‘mind’ and ‘matter’.

Lagrangian submanifolds of the complex hyperbolic quadric

We consider the complex hyperbolic quadric $${Q^*}^n$$ as a complex hypersurface of complex anti-de Sitter space. Shape operators of this submanifold give rise to a family of local almost product structures on $${Q^*}^n$$ , which are then used to define local angle functions on any Lagrangian submanifold of $${Q^*}^n$$ . We prove that a Lagrangian immersion into $${Q^*}^n$$ can be seen as the Gauss map of a spacelike hypersurface of (real) anti-de Sitter space and relate the angle functions to the principal curvatures of this hypersurface. We also give a formula relating the mean curvature of the Lagrangian immersion to these principal curvatures. The theorems are illustrated with several examples of spacelike hypersurfaces of anti-de Sitter space and their Gauss maps. Finally, we classify some families of minimal Lagrangian submanifolds of $${Q^*}^n$$ : those with parallel second fundamental form and those for which the induced sectional curvature is constant. In both cases, the Lagrangian submanifold is forced to be totally geodesic.

Isometric immersions with flat normal bundle between space forms

We investigate the behavior of the second fundamental form of an isometric immersion of a space form with negative curvature into a space form so that the extrinsic curvature is negative. If the immersion has flat normal bundle, we prove that its second fundamental form grows exponentially.

Распад интерсубъективности: безумие как невозможность любви (по Л. Бинсвангеру)

The article considers the problem of love and madness as opposite modes of human existence. Using the example of human interaction with artificial intelligence it has been analyzed from the point of view of the phenomenology of love and Ludwig Binswanger's Dasein analysis the reciprocal influence of madness and disintegration of intersubjectivity in the context of an anthropocrisis. It has been demonstrated that the full realization of a person is impossible in isolation from others, it is possible only in relationships with others, the highest form of which is love. A human being is a born possibility of a "generalized We", his task is to realize this possibility in a direct meeting of "We". Only through "We" can Dasein achieve its fullest realization. Love is defined as the essential structure of the human, the "fundamental form" that structures the human being and its failure causes madness. It has been considered the hypothesis of L. Binswanger about the failure of love in a psychopathological state, in connection with the perception of others as objects and the consequent impossibility of creating "We" as being-in-the-world-together, and about the form of treatment, which consists in opening the possibility of "We". A hypothesis has been put forward that the forced external limitation of the realization of intentionality to "We" can also affect the narrowing of the world-project and lead to madness.

PROPERTIES OF CERTAIN CLASS OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS INVOLVING POLYLOGARITHM FUNCTION

In this work, we introduce a new class of meromorphically starlike functions defined by generalized polylogaritham and investigate coefficient bounds, distortion properties, radius of convexity, convex linear combinations and integral transforms. Furthermore, we obtain partial sums and neigbourhood results for the class also.

Laguerre hypersurfaces with definite Laguerre tensor

x : Mn-1 ? Rn be an umbilical free hypersurface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B, which are invariants of x under Laguerre transformation group. In this paper, we will study the Laguerre hypersurface with parallel Laguerre form and nonnegative or non-positive Laguerre tensor.

Role of Internal Marketing in Determining Academic Staff Job Satisfaction in Higher Education

Purpose-The purpose of the present study is to examine the influence of internal marketing (IM) dimensions (i.e. academic staff development, rewards, internal communication and empowerment) on academic job satisfaction (AJS) in higher education. Design/Methodology/Approach - A survey of 236 faculty members of Jammu division from the UT of J&K higher education institutions was done. To analyse the data SEM has been used. Findings - The results of the study indicated that all the four dimensions of internal marketing significantly influence academic job satisfaction. Empowerment plays the foremost critical part in determining AJS, there after internal communication, academic staff development and rewards. Practical Implications - By highlighting the influence of these four dimensions of IM on AJS, this study offers valuable experiences into the fundamental forms through which job satisfaction among the staff can be improved. The results of this study will demonstrate to be of incredible assistance to academicians and policymakers. They can give their energies and assets towards devising strategies pointed at maximizing faculty satisfaction level through the proper implementation of IM practices. Originality/Value -This study includes to the exceptionally little number of researches that have explored the individual influence of the above mentioned four dimensions of IM in determining AJS.

Target metric and Shell Shaping

Abstract We exploit the possibility of deforming a shell by assigning a target metric, which, for 2D structures, is decomposed into the first and second target fundamental-forms. As well known, an elastic shell may change its shape under two different kinds of actions: one are the loadings, the other one are the distortions, also known as the pre-strains. Actually, the target fundamental forms prescribe a sought shape for the solid, and the metric effectively realized is the one that minimizes the distance, measured through an elastic energy, between the target and the actual fundamental forms. The proposed method is very effective in deforming shells.

Conformal hypersurface geometry via a boundary Loewner–Nirenberg–Yamabe problem

We develop an approach to the conformal geometry of embedded hyper- surfaces by treating them as conformal infinities of conformally compact manifolds. This involves the Loewner-Nirenberg-type problem of finding on the interior a metric that is both conformally compact and of constant scalar curvature. Our first main result is an asymptotic solution to all orders. This involves log terms. We show that the coefficient of the first of these is a hypersurface conformal invariant which gener- alises to higher dimensions the Willmore invariant of embedded surfaces. We call this the obstruction density and for even dimensional hypersurfaces this is a fundamental curvature invariant. We make the latter notion precise and show that the obstruction density and the trace-free second fundamental form are, in a suitable sense, the only such invariants. We also show that this obstruction to smoothness is a scalar density analog of the Fefferman-Graham obstruction tensor for Poincare-Einstein metrics; in part this is achieved by exploiting Bernstein-Gel'fand-Gel'fand machinery. The solu- tion to the constant scalar curvature problem provides a smooth hypersurface defining density determined canonically by the embedding up to the order of the obstruction. We give two key applications: the construction of conformal hypersurface invariants and the construction of conformal differential operators. In particular we present an infinite family of conformal powers of the Laplacian determined canonically by the conformal embedding. In general these depend non-trivially on the embedding and, in contrast to Graham-Jennes-Mason-Sparling operators intrinsic to even dimensional hypersurfaces, exist to all orders. These extrinsic conformal Laplacian powers deter- mine an explicit holographic formula for the obstruction density. We also use these to construct conformally invariant hypersurface functionals. On each even dimensional hypersurface they provide a higher dimensional generalisation of the Willmore energy functional. In particular the functional gradient, with respect to variation of embed- ding, has linear leading term and thus provides another generalisation of the Willmore equation. It agrees with the obstruction density equation at leading derivative order.

A sharp integral inequality for compact Weingarten hypersurfaces under an Okumura type inequality

Our aim in this paper is to provide a sharp integral inequality involving the norm of the traceless second fundamental form of a wide class of compact (without boundary) linear Weingarten hypersurfaces (including those with two distinct principal curvatur

B.-Y. Chen’s inequality for pointwise CR-slant warped products in cosymplectic manifolds

Recently, pointwise CR-slant warped products introduced by Chen and Uddin in [14] for Kaehler manifolds. In the context of almost contact metric manifolds, in this paper, we study these submanifolds in cosymplectic manifolds. We investigate the geometry of such warped product and prove establish a lower bound relation between the second fundamental form and warping function. The equality case is also investigated.

Children’s and Young Adult Comics by Gwen Athene Tarbox

Reviewed by: Children’s and Young Adult Comics by Gwen Athene Tarbox Deborah Brothers (bio) Gwen Athene Tarbox. Children’s and Young Adult Comics. Bloomsbury Academic, 2020. Children’s literature is not the same as young adult literature. “Comics” can mean anything from a one-panel cartoon to a multivolume graphic novel. Each of these fields is impacted by cultural trends as well as deep and challenging assumptions about audience, race, ethnicity, gender, censorship issues, and more. In this slim (just under two hundred pages) volume, Western Michigan University professor Gwen Tarbox unpacks some of those complications for general readers and students yet never reduces the analysis to talking points for scholars. The third book of the Bloomsbury Comics Studies Series, Children and Young Adult Comics invites all to learn from an expert teacher and synthesis magician. Tarbox weaves the complicated strands into a patterned tapestry, creating a “revised history of children’s literature” as she shifts “comics from the periphery to the center of the discussion” (3). Tarbox builds upon earlier work of many scholars (Maria Nikolajeva, Perry Nodelman, and Philip Nel, for example) but also, notably, herself. She and [End Page 132] Michelle Abate broke new ground in their first-of-its-kind Graphic Novels for Children and Young Adults (2017). In Tarbox’s essay from that book, “From Whoville to Hereville: Integrating Graphic Novels into an Undergraduate Children’s Literature Course,” she explains that “no children’s literature textbook to date includes a dedicated chapter on the comics medium” (142). Her current project becomes such a text. Children and Young Adult Comics is redolent with insights from years of teaching and reading critical scholarship pertaining to visual literacy, comics, and children’s literature. The personal focus Tarbox always brings to her own scholarly work, an emphasis on equity and inclusion, is manifestly present and developed in a manner that satisfies like the last piece of a jigsaw puzzle. The “Introduction” (chapter 1) reveals comics’ capacity to reach diverse audiences, even as their champions employed Superhero qualities in order to secure their place in literary conversations. Comics, Tarbox tells us, have only been seen as “an aesthetically and a pedagogically valid form of expression” by “most librarians, teachers, and publishers” since the turn of the twenty-first century (2). The fact that comics are recognized as important and what this recognition means to the fields of children’s and young adult literature are further taken up the next four chapters of the book. Chapter 2, “Historical Overview,” carefully bridges the parallel worlds of comics as a medium and children’s literature as a field, displaying how illustration has long been associated with children’s books, so when comic books became popularized and marketed to children beginning in the 1930s, a two-decade or so love affair between classic texts and comic book depictions was born. This, in turn, birthed a readership that included children and young adults in novel ways (27). The relationship between producers, marketers, and readers intersected and influenced each other, even when few people, outside of those marketing to children, saw the relationship as positive. Chapter 3, “Social and Cultural Impact,” depicts how the history still impacts the assumptions behind children’s publishing. Each section of this small book brings intellectual surprise, but chapter 4, “Critical Uses,” packs the largest pedagogical punch for those newer to comics form analysis because it is here that her pedagogical applications are best displayed. In the chapter’s “Case Study” sections, Tarbox models activities that build fundamental form literacy and reflective analysis for any comics enthusiast or children’s lit lover. Instructors (for students of any age) can use the suggested texts or apply the techniques to other comics, adapting exercises on closure, braiding, image/text relationships, focalization, point of view, line style, and color (83–108). Tarbox’s work in the section on “Manga” (108–11) adds much needed context for those who are looking to go beyond a surface-level reading. [End Page 133] Throughout the book, Tarbox thoroughly displays how Nodelman’s 1999 assertion that picture books must be decoded using the convergence of text with pictures holds true with comics as well, and this core...

Symmetric convex sets with minimal Gaussian surface area

Let $\Omega\subset\Bbb{R}^{n+1}$ have minimal Gaussian surface area among all sets satisfying $\Omega=-\Omega$ with fixed Gaussian volume. Let $A=A_x$ be the second fundamental form of $\partial\Omega$ at $x$, i.e., $A$ is the matrix of first order partial derivatives of the unit normal vector at $x\in\partial\Omega$. For any $x=(x_1,\ldots,x_{n+1})\in\Bbb{R}^{n+1}$, let $\gamma_n(x)=(2\pi)^{-n/2}e^{-(x_1^2+\cdots+x_{n+1}^2)/2}$. Let $\|A\|^{2}$ be the sum of the squares of the entries of $A$, and let $\|A\|_{2\to 2}$ denote the $\ell_{2}$ operator norm of $A$.

Zamknięte stolice imperium prawa. Znaczenie jawności postępowań sądowych dla społecznej legitymizacji władzy sądowniczej

Closed capitals of the empire of law. The importance of openness of judicial proceedings for social legitimacy of judicial authority The article focuses on the openness of judicial proceedings, in particular the openness of the trial, considered as an important element of the constitutional right to a trial, the requirement of procedural fairness and the condition for maintaining the social legitimacy of the judiciary. The immediate context for the considerations is determined by the changes introduced by the Act of May 28, 2021 amending the Act – the Polish Code of Civil Procedure and certain other acts, making it possible to limit the openness of court proceedings in relation to the occurrence of an epidemiological emergency. The author draws the attention to transformations in the constitutional position and ways of perceiving the legitimacy of courts in modern constitutional democracies. The increasing role of courts in settling major political disputes, resolving social conflicts, controlling governmental authorities and enabling citizens to hold representatives of the authorities accountable for their decisions renders participation in judicial proceedings one of the fundamental democratic activities nowadays. The author also indicates that the trial (as a fundamental form of communication between judges and citizens and a special phase of proceedings allowing the court to deeply examine the facts of the case and to learn the prevailing understanding among citizens of the values and principles on which the legal order is based) is a key measure to achieve the principles of procedural justice during the course of specific proceedings and to establish trust in the third power before the public. Openness of judicial proceedings, especially the trial, is a condition for the courts to maintain a reflexive attitude in the process of ruling and thus to deepen the social legitimacy of the judiciary based on trust.

Importance of the principles of criminal law in the classification of crimes

The correct qualification of a crime provides the basis for achieving the goals of criminal liability, including sentencing a just punishment. During qualification, law enforcement agencies (investigative bodies, inquiry bodies, and court) often face problems caused by contradictions in criminal law regulation (a gap in law, defects in law, legal conflicts, evaluation categories of law, etc.). According to the authors, it is possible to eliminate the contradictions of criminal law regulation by applying the principles of criminal law as a direct regulator of criminal law relations. Purpose of the research: to identify the problems of qualifying crimes in the modern practice of preliminary investigation bodies and courts, as well as to determine the place and role of the principles of criminal law in the process. Framework of the research. The research was carried out with general scientific methods (dialectical, statistical, comparative legal); in addition, methods of analysis, deduction, synthesis, as well as a formally legal method, were used in the research. Conclusions: the authors draw the conclusion that the principles of criminal law should be considered as an independent fundamental form of Russian law.

Referendum in the Slovak Republic. Theory and Practice

This article deals with the fundamental form of direct democracy – a referendum in terms of its constitutional regulation and practical implementation in the Slovak Republic. It analyses the constitutional concept of the referendum with an emphasis on its legislative development and practical implementation within the functioning of the independent state after the year 1993. It points out some interpretative problems arising from the application practice and examines its constitutional implications relying on the relevant case law of the Constitutional Court of the Slovak Republic.

A STUDY ON THE HARMONIC EVOLUTE SURFACES OF QUASI BINORMAL SURFACES

In this paper, harmonic evolute surface of quasi binormal surface associated with quasi frame is studied. After constructing quasi binormal surface, we determine harmonic evolute surface of quasi binormal surface by using first and second fundamental forms. We then obtain some new results about these new surfaces and give some applications for them.