On the strong uniqueness of minimal projections in the space $l_\\infty^9$

В работе рассматриваются минимальные проекции пространства $l_\\infty^9$ на некоторые подпространства коразмерности 3. Для них найдены относительные прекционные константы, а в случае минимальной проекции с единичной нормой найдено максимальной значение константы сильной единственности. Найденые проекционные константы могут найти применение в вычислительной математике, в частности, для оценки сходимости проекционных методов решения операторных уравнений и в оценках ошибки алгоритма Ремеза. In this paper we consider minimal projections of the space $l_\\infty^9$ on some subspaces of codimension 3. Relative projection constants are found for them, and in the case of a minimal projection with a unit norm, we find maximum value of the strong uniqueness constant.

Permeation of β-Lactamase Inhibitors through the General Porins of Gram-Negative Bacteria

Modern medicine relies upon antibiotics, but we have arrived to the point where our inability to come up with new effective molecules against resistant pathogens, together with the declining private investment, is resulting in the number of untreatable infections increasing worldwide at worrying pace. Among other pathogens, widely recognized institutions have indicated Gram-negative bacteria as particularly challenging, due to the presence of the outer membrane. The very first step in the action of every antibiotic or adjuvant is the permeation through this membrane, with small hydrophilic drugs usually crossing through protein channels. Thus, a detailed understanding of their properties at a molecular level is crucial. By making use of Molecular Dynamics simulations, we compared the two main porins of four members of the Enterobacteriaceae family, and, in this paper, we show their shared geometrical and electrostatic characteristics. Then, we used metadynamics simulations to reconstruct the free energy for permeation of selected diazobicyclooctans through OmpF. We demonstrate how porins features are coupled to those of the translocating species, modulating their passive permeation. In particular, we show that the minimal projection area of a molecule is a better descriptor than its molecular mass or the volume. Together with the magnitude and orientation of the electric dipole moment, these are the crucial parameters to gain an efficient compensation between the entropic and enthalpic contributions to the free energy barrier required for permeation. Our results confirm the possibility to predict the permeability of molecules through porins by using a few molecular parameters and bolster the general model according to which the free energy increase is mostly due to the decrease of conformational entropy, and this can be compensated by a favorable alignment of the electric dipole with respect to the channel intrinsic electric field.

Uniqueness of minimal projections in smooth expanded matrix spaces

Let us consider the space M(n, m) of all real or complex matrices on n rows and m columns. In 2000 Lesław Skrzypek proved the uniqueness of minimal projection of this space onto its subspace $$M(n,1)+M(1,m)$$ M ( n , 1 ) + M ( 1 , m ) which consists of all sums of matrices with constant rows and matrices with constant columns. We generalize this result using some new methods proved by Lewicki and Skrzypek (J Approx Theory 148:71–91, 2007). Let S be a space of all functions from $$X\times Y \times Z$$ X × Y × Z into $${\mathbb {R}}$$ R or $${\mathbb {C}}$$ C , where X, Y, Z are finite sets. It could be interpreted as a space of three-dimensional matrices M(n, m, r). Let T be a subspace of S consisting of all sums of functions which depend on one variable. Let S be equipped with a smooth norm $$\Vert .\Vert $$ ‖ . ‖ . We show that there exists the unique minimal projection of S onto its subspace T.

The Mexican Son , Past and Present

Among the many musical traditions of Mexico, the son is one of the most representative of the richness and diversity of Mexican culture. Son (or sones) is a generic term that describes both a complex of genres and the various regional subgenres that make up that complex. Son is a type of traditional music performed by small ensembles, with or without singing, and danced. It serves to entertain, but is also performed at celebratory occasions and festivals as well as in rituals. Although sones appear throughout Mexico marked by regional differences in both instrumentation and performance styles, they share common characteristics that define the genre as a whole, musically (i.e., their rhythmic, melodic, and harmonic structures), lyrically, and choreographically. Because of the particular cultural traits and sociocultural contexts that each son subgenre encompasses, it can be argued that regional sones are a powerful expression of Mexican regional musics, cultures, and social identities. Born as a hybrid genre out of the intermixing of European, American Indian, African, and Afro-Caribbean musical elements and contexts, Mexican sones have moved through time defined by many as a symbol of Mexican identity, even if the very concept of that “Mexican identity” has changed over time. What might be called the son’s “Golden Age” lasted from the 1890s until the middle of the 20th century. By the 1960s, sones were in serious decline all around Mexico: they had lost the favor of their audiences, old performers had passed away, and new generations did not engage with these musical traditions. Cultural politics contributed to selective processes through which some son subgenres faded away. Sociopolitical processes from the 1930s to the 1980s contributed to the re-contextualization of the Mexican son through modified versions of sones staged and broadcast in theatres, radio stations, and film productions. Post-revolutionary nationalism, the music industry, and folkloric ballets created these new versions and exercised an ideological control that both affected popular musical expressions and shaped musical tastes. Changes in urbanization and life conditions transformed social relationships and furthered this intense transformation. With fewer performance occasions and little support from either the government or private patrons, several regional son subgenres became thin and isolated, with minimal projection outside their regions. In the 1980s, some of the son subgenres underwent a renaissance owing to various private and official initiatives that infused new life to the music. This article provides an overview of the son, past and present, connecting the relevance of this musical style with the social history of the country.

Resolving the Issue of the Target of Vowel Copy in Fijian Loanwords

English loanwords into Fijian undergo vowel epenthesis, as Fijian disallows coda consonants and consonant clusters. Vowel copy is an option for determining epenthetic vowel quality in loanword adaptation (Kumagai 2016a; Schütz 1978, 2004). The target of copy epenthesis seems to be either the preceding or following vowel of the epenthetic site. However, the choice of target vowel is indeterminate, as there is no vowel copy in Fijian native phonology. This paper offers a resolution to the problem by adopting an expanded version of prosodic projection theory (Martínez-Paricio 2012, 2013), in which feet are allowed to exhibit maximal/minimal projection. I propose Foot Condition, which requires the Foot[±max/±min] to circumscribe the vowel copy domain.

Extension of Bessel sequences to oblique dual frame sequences and the minimal projection

An extension of two Bessel sequences to oblique dual frame sequences and its applications to shift-invariant spaces are considered. The best-known situation where this kind of extension is necessary is the construction of a pair of biorthogonal multiresolution analyses, where two generating sets whose shifts are only assumed to be Bessel sequences are given. This extension naturally leads to consideration of the ‘minimal projection’ extending two closed subspaces. The existence or non-existence of the minimal projection is discussed.