Concurrent π\pi-vector fields and energy beta-change

The present paper deals with an \emph{intrinsic} investigation of the notion of a concurrent $\pi$-vector field on the pullback bundle of a Finsler manifold $(M,L)$. The effect of the existence of a concurrent $\pi$-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular $\beta$-change, namely the energy $\beta$-change ($\widetilde{L}^{2}(x,y)=L^{2}(x,y)+ B^{2}(x,y) with \ B:=g(\bar{\zeta},\bar{\eta})$;$\bar{\zeta} $being a concurrent$\pi$-vector field), is established. The relation between the two Barthel connections$\Gamma$and$\widetilde{\Gamma}$, corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy$\beta$-change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is concluded. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.Comment: 27 pages, LaTex file, Some typographical errors corrected, Some formulas simpifie

Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

The importance of Einstein's geometrization philosophy, as an alternative to the least action principle, in constructing general relativity (GR), is illuminated. The role of differential identities in this philosophy is clarified. The use of Bianchi identity to write the field equations of GR is shown. Another similar identity in the absolute parallelism geometry is given. A more general differential identity in the parameterized absolute parallelism geometry is derived. Comparison and interrelationships between the above mentioned identities and their role in constructing field theories are discussed.Comment: LaTeX file, 17 pages, comments and criticism are welcom

Generalized β\beta-conformal change and special Finsler spaces

In this paper, we investigate the change of Finslr metrics $$L(x,y) \to\bar{L}(x,y) = f(e^{\sigma(x)}L(x,y),\beta(x,y)),$$ which we refer to as a generalized $\beta$-conformal change. Under this change, we study some special Finsler spaces, namely, quasi C-reducible, semi C-reducible, C-reducible, $C_2$-like, $S_3$-like and $S_4$-like Finsler spaces. We also obtain the transformation of the T-tensor under this change and study some interesting special cases. We then impose a certain condition on the generalized $\beta$-conformal change, which we call the b-condition, and investigate the geometric consequences of such condition. Finally, we give the conditions under which a generalized $\beta$-conformal change is projective and generalize some known results in the literature.Comment: References added, some modifications are performed, LateX file, 24 page

On Finslerized Absolute Parallelism spaces

The aim of the present paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism space (GAP-space). The Finsler structure is obtained from the vector fields forming the parallelization of the GAP-space. The resulting space, which we refer to as a Finslerized Parallelizable space, combines within its geometric structure the simplicity of GAP-geometry and the richness of Finsler geometry, hence is potentially more suitable for applications and especially for describing physical phenomena. A study of the geometry of the two structures and their interrelation is carried out. Five connections are introduced and their torsion and curvature tensors derived. Some special Finslerized Parallelizable spaces are singled out. One of the main reasons to introduce this new space is that both Absolute Parallelism and Finsler geometries have proved effective in the formulation of physical theories, so it is worthy to try to build a more general geometric structure that would share the benefits of both geometries.Comment: Some references added and others removed, PACS2010, Typos corrected, Amendemrnts and revisions performe

Consistency, Amplitudes and Probabilities in Quantum Theory

Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This constraint is expressed in the form of functional equations the solution of which leads to the usual sum and product rules for amplitudes. A consequence is that the Schrodinger equation must be linear: non-linear variants of quantum mechanics are inconsistent. The physical interpretation of the theory is given in terms of a single natural rule. This rule, which does not itself involve probabilities, is used to obtain a proof of Born's statistical postulate. Thus, consistency leads to indeterminism. PACS: 03.65.Bz, 03.65.Ca.Comment: 23 pages, 3 figures (old version did not include the figures

On dimension reduction in Gaussian filters

A priori dimension reduction is a widely adopted technique for reducing the computational complexity of stationary inverse problems. In this setting, the solution of an inverse problem is parameterized by a low-dimensional basis that is often obtained from the truncated Karhunen-Loeve expansion of the prior distribution. For high-dimensional inverse problems equipped with smoothing priors, this technique can lead to drastic reductions in parameter dimension and significant computational savings. In this paper, we extend the concept of a priori dimension reduction to non-stationary inverse problems, in which the goal is to sequentially infer the state of a dynamical system. Our approach proceeds in an offline-online fashion. We first identify a low-dimensional subspace in the state space before solving the inverse problem (the offline phase), using either the method of "snapshots" or regularized covariance estimation. Then this subspace is used to reduce the computational complexity of various filtering algorithms - including the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within a novel subspace-constrained Bayesian prediction-and-update procedure (the online phase). We demonstrate the performance of our new dimension reduction approach on various numerical examples. In some test cases, our approach reduces the dimensionality of the original problem by orders of magnitude and yields up to two orders of magnitude in computational savings

Valorization of wine‐making by‐products’ extracts in cosmetics

The increased demand for conscious, sustainable and beneficial products by the consumers has pushed researchers from both industries and universities worldwide to search for smart strategies capable of reducing the environmental footprint, especially the ones connected with industrial wastes. Among various by-products, generally considered as waste, those obtained by winemaking industries have attracted the attention of a wide variety of companies, other than the vineries. In particular, grape pomaces are considered of interest due to their high content in bioactive molecules, especially phenolic compounds. The latter can be recovered from grape pomace and used as active ingredients in easily marketable cosmetic products. Indeed, phenolic compounds are well known for their remarkable beneficial properties at the skin level, such as antioxidant, antiaging, anti-hyperpigmentation and photoprotective effects. The exploitation of the bioactives contained in grape pomaces to obtain high value cosmetics may support the growing of innovative start-ups and expand the value chain of grapes. This review aims to describe the strategies for recovery of polyphenols from grape pomace, to highlight the beneficial potential of these extracts, both in vitro and in vivo, and their potential utilization as active ingredients in cosmetic products

Effects of Color Attributes on Trap Capture Rates of Chrysobothris femorata (Coleoptera: Buprestidae) and Related Species

Chrysobothris spp. (Coleoptera: Buprestidae) and other closely related buprestids are common pests of fruit, shade, and nut trees in the United States. Many Chrysobothris spp., including Chrysobothris femorata, are polyphagous herbivores. Their wide host range leads to the destruction of numerous tree species in nurseries and orchards. Although problems caused by Chrysobothris are well known, there are no reliable monitoring methods to estimate local populations before substantial damage occurs. Other buprestid populations have been effectively estimated using colored sticky traps to capture beetles. However, the attraction of Chrysobothris to specific color attributes has not been directly assessed. A multi-color trapping system was utilized to determine color attraction of Chrysobothris spp. Specific color attributes (lightness [L*], red to green [a*], blue to yellow [b*], chroma [C*], hue [h*], and peak reflectance [PR]) were then evaluated to determine beetle responses. In initial experiments with mostly primary colors, Chrysobothris were most attracted to traps with red coloration. Thus, additional experiments were performed using a range of trap colors with red reflectance values. Among these red reflectance colors, it was determined that the violet range of the electromagnetic spectrum had greater attractance to Chrysobothris. Additionally, Chrysobothris attraction correlated with hue and b*, suggesting a preference for traps with hues between red to blue. However, males and females of some Chrysobothris species showed differentiated responses. These findings provide information on visual stimulants that can be used in Chrysobothris trapping and management. Furthermore, this information can be used in conjunction with ecological theory to understand host-location methods of Chrysobothris