An approximate Hahn–Banach theorem for positively homogeneous functions

This note provides an approximate version of the Hahn–Banach theorem for non-necessarily convex extended-real valued positively homogeneous functions of degree one. Given p : X → R∪{+∞} such a function defined on the real vector space X, and a linear function defined on a subspace V of X and dominated by p (i.e. (x) ≤ p(x) for all x ∈ V), we say that can approximately be p-extended to X, if is the pointwise limit of a net of linear functions on V, every one of which can be extended to a linear function defined on X and dominated by p. The main result of this note proves that can approximately be p-extended to X if and only if is dominated by p∗∗, the pointwise supremum over the family of all the linear functions on X which are dominated by p.

Wannier functions of a one-dimensional photonic crystal with inversion symmetry

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Certain problems concerning polynomials and transcendental entire functions of exponential type

Soit $\displaystyle P(z):=\sum_{\nu=0}^na_\nu z^{\nu}$ un polynôme de degré $n$ et $\displaystyle M:=\sup_{|z|=1}|P(z)|.$ Sans aucne restriction suplémentaire, on sait que $|P'(z)|\leq Mn$ pour $|z|\leq 1$ (inégalité de Bernstein). Si nous supposons maintenant que les zéros du polynôme $P$ sont à l'extérieur du cercle $|z|=k,$ quelle amélioration peut-on apporter à l'inégalité de Bernstein? Il est déjà connu [{\bf \ref{Mal1}}] que dans le cas où $k\geq 1$ on a $$(*) \qquad |P'(z)|\leq \frac{n}{1+k}M \qquad (|z|\leq 1),$$ qu'en est-il pour le cas où $k < 1$? Quelle est l'inégalité analogue à $(*)$ pour une fonction entière de type exponentiel $\tau ?$ D'autre part, si on suppose que $P$ a tous ses zéros dans $|z|\geq k \, \, (k\geq 1),$ quelle est l'estimation de $|P'(z)|$ sur le cercle unité, en terme des quatre premiers termes de son développement en série entière autour de l'origine. Cette thèse constitue une contribution à la théorie analytique des polynômes à la lumière de ces questions.

Spectral functions of half-filled one-dimensional Hubbard rings with varying boundary conditions

We study the effect of varying the boundary condition on: the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow-which spans the whole Brillouin zone-and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.

Wannier functions of isolated bands in one-dimensional crystals

We present a simple procedure to obtain the maximally localized Wannier function of isolated bands in one-dimensional crystals with or without inversion symmetry. First, we discuss the generality of dealing with real Wannier functions. Next, we use a transfer-matrix technique to obtain nonoptimal Bloch functions which are analytic in the wave number. This produces two classes of real Wannier functions. Then, the minimization of the variance of the Wannier functions is performed, by using the antiderivative of the Berry connection. In the case of centrosymmetric crystals, this procedure leads to the Wannier-Kohn functions. The asymptotic behavior of the Wannier functions is also analyzed. The maximally localized Wannier functions show the expected exponential and power-law decays. Instead, nonoptimal Wannier functions may show reduced exponential and anisotropic power-law decays. The theory is illustrated with numerical calculations of Wannier functions for conduction electrons in semiconductor superlattices.

On the calculation of inner products of Schur functions

Two methods for calculating inner products of Schur functions in terms of outer products and plethysms are given and they are easy to implement on a machine. One of these is derived from a recent analysis of the SO(8) proton-neutron pairing model of atomic nuclei. The two methods allow for generation of inner products for the Schur functions of degree up to 20 and even beyond.

Thermal behavior of cellulose acetate produced from homogeneous acetylation of bacterial cellulose

Cellulose acetate (CA) is one of the most important cellulose derivatives and its main applications are its use in membranes, films, fibers, plastics and filters. CAs are produced from cellulose sources such as: cotton, sugar cane bagasse, wood and others. One promissory source of cellulose is bacterial cellulose (BC). In this work, CA was produced from the homogeneous acetylation reaction of bacterial cellulose. Degree of substitution (DS) values can be controlled by the acetylation time. The characterization of CA samples showed the formation of a heterogeneous structure for CA samples submitted to a short acetylation time. A more homogeneous structure was produced for samples prepared with a long acetylation time. This fact changes the thermal behavior of the CA samples. Thermal characterization revealed that samples submitted to longer acetylation times display higher crystallinity and thermal stability than samples submitted to a short acetylation time. The observation of these characteristics is important for the production of cellulose acetate from this alternative source. (C) 2008 Elsevier B.V. All rights reserved.

Effects of square-stepping exercise on cognitive functions of older people

Aim: Cognitive functions can decline with age, and interventions focusing on stimulating them may have positive results. Previous studies have shown that square-stepping exercise (SSE) has a good influence on balance, but this exercise also seems to promote cognitive stimulation. Therefore, the purpose of the present study was to analyse the effect of 16 weeks of SSE on cognitive functions in non-demented community-dwelling older people. Methods: This was a longitudinal, non-randomized study. Forty-one older adults (60 years and older) were recruited, and 21 participated in the SSE group (practised only SSE sequences) and 20 were in the control group (continued with their activities of daily living). Both groups were evaluated using the Mini-Mental State Examination, the Digit Span test, the Toulouse-Pierón Attention Test and the Modified Card Sorting Test. Results: The SSE group showed a significant improvement in global cognitive status, concentrated attention and mental flexibility after 16 weeks of the SSE intervention. Conclusion: Evidence shows that SSE is a physical activity that positively influences cognitive functions in non-demented older people. © 2013 Japanese Psychogeriatric Society.

Tables of Bessel-Clifford functions of orders zero and one.

Mode of access: Internet.

A treatise on the integral calculus : containing the integration of explicit functions of one variable ; together with the theory of definite integrals and of elliptic functions /

Mode of access: Internet.

Indefinite determiner introducing definite referent: a special use of 'yi 'one' + classifier' in Chinese

The indefinite determiner yi 'one'+ classifier' is the most approximate to an indefinite article, like the English a, in Chinese. It serves all the functions characteristic of representative stages of grammaticalization from a numeral to a generalized indefinite determiner as elaborated in the literature. It is established in this paper that the Chinese indefinite determiner has developed a special use with definite expressions, serving as a backgrounding device marking entities as of low thematic importance and unlikely to receive subsequent mentions in ensuing discourse. 'yi+ classifier' in the special use with definite expressions displays striking similarities in terms of semantic bleaching and phonological reduction with the same determiner at the advanced stage of grammaticalization characterized by uses with generics, nonspecifics and nonreferentials. An explanation is offered in terms of an implicational relation between nonreferentiality and low thematic importance which characterize the two uses of the indefinite determiner. While providing another piece of evidence in support of the claim that semantically nonreferentials and entities of low thematic importance tend to be encoded in terms of same linguistic devices in language, findings in this paper have shown how an indefinite determiner can undergo a higher degree of grammaticalization than has been reported in the literature-it expands its scope to mark not only indefinite but also definite expressions as semantically nonreferential and/or thematically unimportant. (C) 2003 Elsevier B.V. All rights reserved.

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

Design and development of a one-degree-of-freedom force-reflecting manual controller prototype for teleoperation

The present research is carried out from the viewpoint of primarily space applications where human lives may be in danger if they are to work under these conditions. This work proposes to develop a one-degree-of-freedom (1-DOF) force-reflecting manual controller (FRMC) prototype for teleoperation, and address the effects of time delays commonly found in space applications where the control is accomplished via the earth-based control stations. To test the FRMC, a mobile robot (PPRK) and a slider-bar were developed and integrated to the 1-DOF FRMC. The software developed in Visual Basic is able to telecontrol any platform that uses an SV203 controller through the internet and it allows the remote system to send feedback information which may be in the form of visual or force signals. Time delay experiments were conducted on the platform and the effects of time delay on the FRMC system operation have been studied and delineated.

Modal functions of future tenses in French

The paper disputes two influential claims in the Romance Linguistics literature. The first is that the synthetic future tenses in spoken Western Romance are now rivalled, if not supplanted, as temporal functors by the more recently developed GO futures. The second is that these synthetic futures now have modal rather than temporal meanings in spoken Romance. These claims are seen as reflecting a universal cycle of diachronic change, in which verb forms originally expressing modal (or aspectual) values take on future temporal reference, becoming tenses. The new modal meanings supplant the temporal, which are then taken up by new forms. Challenges to this theory for French are raised on the basis of empirical evidence of two sorts. Positively, future tenses in spoken Romance continue to be used with temporal meaning. Negatively, evidence of modal meaning for these forms is lacking. The evidence comes froma corpora of spoken French, native speaker judgements and verb data from a daily broadsheet. Cumulatively, it points to the reverse of the claims noted above: the synthetic future in spoken French has temporal but little modal meaning.