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In this paper we establish boundedness and continuity results for vectorial local minimizers of special classes of integral functionals. In particular we consider a class of vectorial problems in which the energy density satisfies fully anisotropic growth. We analyze two different types of anisotropic growths connected with the Orlicz Sobolev spaces. We prove boundedness results for energy densities satisfying anisotropic growth, moreover for particular energy densities we get Hölder continuity results by proving that each component belongs to a suitable De Giorgi class. Finally, we provide specific non-trivial instances of our results. [ABSTRACT FROM AUTHOR]

In this paper we study the everywhere Hölder continuity of the minima of the following class of vectorial integral functionals ∫ Ω ∑ α = 1 n f α x , u α , ∇ u α + G x , u , ∇ u d x The energy densities satisfy suitable structure assumptions and may have neither radial nor quasi-diagonal structure. The regularity of minimizers is obtained by proving that each component stays in a suitable De Giorgi class and, from this, we conclude about the Hölder continuity. [ABSTRACT FROM AUTHOR]

In this paper we prove local Hölder continuity of vectorial local minimizers of special classes of integral functionals with rank-one and polyconvex integrands. The energy densities satisfy suitable structure assumptions and may have neither radial nor quasi-diagonal structure. The regularity of minimizers is obtained by proving that each component stays in a suitable De Giorgi class and, from this, we conclude about the Hölder continuity. In the final section, we provide some non-trivial applications of our results.

Background: Age‐related attenuation of the orbital, zygomatic, and masseteric ligaments contribute to temporal brow ptosis, deepening nasolabial fold, and jowl, respectively. Aims: To present and assess the vectorial facial sculpting (VFS) technique, a novel nonsurgical panfacial rejuvenation method which focuses on reversal of the impact of attenuated ligaments on the aging face. Methods: This case series included women who underwent vectorial facial sculpting at a private clinic from June 2018 to January 2019. Sagging tissues in the lateral brow, nasolabial fold, and jowl were repositioned in a directed manner with vectors whose cross‐product counteracted the vector of the respective causative attenuated ligament. Filler material was deposited into the supraperiosteal/sub‐SMAS plane in right angle vectors at the lateral supra‐orbital rim for brow ptosis, pre‐auricular and malar region for nasolabial fold and across the jawline region for jowl. Standardized photographs were taken before and at 3 months following treatment. Outcome was assessed by both the patients and an independent investigator using a validated Global Aesthetic Improvement Scale. Adverse outcomes were documented. Results: Forty‐five patients of mean age 59.8 ± 3.9 years were included. Mean Global Aesthetic Improvement Scale scores for patients and an independent investigator alike at 3 months following treatment indicated "very much improved" (1.44 ± 0.66 and 1.56 ± 0.78, respectively). The procedure was well tolerated with no adverse events. Conclusion: Vectorial facial sculpting is a comprehensive anatomical approach for nonsurgical directional tissue mobilization. Based on physical and mathematical rules to reverse the respective causative attenuated ligament, the technique effectively and safely restores youthful facial contours. [ABSTRACT FROM AUTHOR]

Algorithm, presented in the article, demonstrates an effective model of processing of vectorial objects in GIS, in particular visualization

The model is reformulated by means of stochastic differential equations, and the parametersare estimated by a maximum likelihood method.VESILIND (1968; 1979) proposed a sludge settling velocity model of exponential form. During recent years,several refinements to the original model have been proposed, see e.g. GRIJSPEERDT et al. (1995); DUPONTand DAHL (1995) EKAMA et al. (1997). In the proposed models several layers in the settling tank areincorporated to permit the calculation of SS profiles over the tank depth and predict the SS concentrations in thereturn sludge and in the effluent from the clarifier.Here, the original VESILIND model combined with a simple suction depth model is used to enable predictionof the SS concentration in the effluent from the tank. In order to make the model applicable for real time controlpurposes, only two layers of variable height in the tank are considered

Scientific argumentation of the permanent reversion into the synthesizing tendency, to purification and simplification of the plastic – sculptural form, along the history of the art. The privilege of the form to periodically gain its freedom by the creative imagination of the artist, by the need to give always a new plastic sense to the "line of the absolute return", either on own account, or in the name of a new aesthetics, crossing over parallel worlds in the eagerness to become elementary and simple. [ABSTRACT FROM AUTHOR]

Introduction: Intestinal epithelial cells represent an important component of innate immunity, with sophisticated responses to inflammatory stimuli. The manner in which intestinal epithelial cell polarity affects responses to inflammatory stimuli is largely unknown. We hypothesized that polarized intestinal epithelial cells exhibit a bidirectional inflammatory response dependent upon the location of the stimulus.Methods: Caco-2 cells were grown on semi-permeable inserts in a dual-compartment culture system and treated with tumor necrosis factor-α (TNF-α; 100 ng/ml) or serum-free media in the apical or basolateral chamber. Interleukin-8 (IL-8) production in each chamber was measured by enzyme-linked immunosorbent assay. To determine receptor specificity, anti-TNF receptor antibodies were added to the apical or basolateral chamber.Results: Basolateral stimulation with TNF-α resulted in increased apical and basolateral IL-8 production. Apical TNF-α stimulation resulted in increased apical, but not basolateral IL-8 production. Receptor blockade suggested TNF receptor 1 involvement on both apical and basolateral membranes, while TNF receptor 2 was only active on the apical membrane.Conclusion: Polarized intestinal epithelial cells respond to TNF-α stimulation with focused, directional secretion of the proinflammatory cytokine IL-8. These findings are important because they suggest that intestinal epithelial cells are capable of organizing their response to inflammatory signals and producing inflammatory mediators in a bidirectional, vectorial fashion. [ABSTRACT FROM AUTHOR]

Starting from the vectorial Rayleigh-Sommerfeld diffraction integrals, the analytical propagation expressions of vectorial nonparaxial Hermite-cosine-Gaussian (HCosG) beams in free space are derived. The on-axis intensity, far-field equation and, in particular, paraxial expressions are given and treated as special cases of our result. It is shown that for vectorial nonparaxial HCosG beams, the parameter f = 1/kw0, with k being the wave number and w0 being the waist width, determines their nonparaxiality. What is more, the decentered parameter also affects their intensity distribution and nonparaxial behavior. The calculation results indicate that the position of maximum on-axis intensity changes with the mode indices. [ABSTRACT FROM AUTHOR]

Physiological studies led to devise models of epithelial cells in which the membrane does not have its molecules distributed homogeneously, but polarized towards the apical or towards the basolateral regions. For a while, it was assumed that the TJ, acting as a fence between the two regions, would be responsible for this asymmetry. However, today the information available indicates not only that polarization may proceed independently of the TJ, but that this structure itself may attain its precise location due to a polarization process. Nevertheless, TJs may play a role in restricting to the apical or to the basolateral region those molecules that are free to diffuse in the plane of the cell membrane (e.g., lipids and protein that are not attached to cytoplasmic or extracellular structures). [ABSTRACT FROM AUTHOR]

The model is reformulated by means of stochastic differential equations, and the parameters are estimated by a maximum likelihood method. VESILIND (1968; 1979) proposed a sludge settling velocity model of exponential form. During recent years, several refinements to the original model have been proposed, see e.g. GRIJSPEERDT et al. (1995); DUPONT and DAHL (1995) EKAMA et al. (1997). In the proposed models several layers in the settling tank are incorporated to permit the calculation of SS profiles over the tank depth and predict the SS concentrations in the return sludge and in the effluent from the clarifier. Here, the original VESILIND model combined with a simple suction depth model is used to enable prediction of the SS concentration in the effluent from the tank. In order to make the model applicable for real time control purposes, only two layers of variable height in the tank are considered. [ABSTRACT FROM AUTHOR]

We know very little about how the cellular environment affects protein folding mechanisms. Here, we focus on one unique aspect of that environment that is difficult to recapitulate in the test tube: the effect of a folding vector. When protein folding is initiated at one end of the polypeptide chain, folding starts from a much smaller ensemble of conformations than during refolding of a full-length polypeptide chain. But to what extent can vectorial folding affect protein folding kinetics and the conformations of folding intermediates? We focus on recent studies of autotransporter proteins, the largest class of virulence proteins from pathogenic Gram-negative bacteria. Autotransporter proteins are secreted across the bacterial inner membrane from N→C-terminus, which, like refolding in vitro , retards folding. But in contrast, upon C→N-terminal secretion across the outer membrane autotransporter folding proceeds orders of magnitude faster. The potential impact of vectorial folding on the folding mechanisms of other proteins is also discussed.