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

Calli Essential Oils Synergize with Lawsone against Multidrug Resistant Pathogens.

The fast development of multi-drug resistant (MDR) organisms increasingly threatens global health and well-being. Plant natural products have been known for centuries as alternative medicines that can possess pharmacological characteristics, including antimicrobial activities. The antimicrobial activities of essential oil (Calli oil) extracted from the Calligonum comosum plant by hydro-steam distillation was tested either alone or when combined with lawsone, a henna plant naphthoquinone, against MDR microbes. Lawsone showed significant antimicrobial activities against MDR pathogens in the range of 200-300 µg/mL. Furthermore, Calli oil showed significant antimicrobial activities against MDR bacteria in the range of 180-200 µg/mL, Candida at 220-240 µg/mL and spore-forming Rhizopus fungus at 250 µg/mL. Calli oil's inhibition effect on Rhizopus, the major cause of the lethal infection mucormycosis, stands for 72 h, followed by an extended irreversible white sporulation effect. The combination of Calli oil with lawsone enhanced the antimicrobial activities of each individual alone by at least three-fold, while incorporation of both natural products in a liposome reduced their toxicity by four- to eight-fold, while maintaining the augmented efficacy of the combination treatment. We map the antimicrobial activity of Calli oil to its major component, a benzaldehyde derivative. The findings from this study demonstrate that formulations containing essential oils have the potential in the future to overcome antimicrobial resistance

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

GC-MS Analysis, Antioxidant, Antimicrobial and Anticancer Activities of Extracts from Ficus sycomorus Fruits and Leaves

Higher plants have been utilized worldwide as characteristic drug a long time to cure human diseases. About 80% of individuals globally use plants as safe sources of medication to cure human diseases through completely different medicine system. One of the available indigenous medicinal plants, Ficus sycomorus belongs to the Moraceae family. The plant contains totally different teams of biologically active compounds that square measure chargeable for the biological activity. Ethanolic and ethyl acetate extracts of leaves of Ficus sycomorus contain higher concentrations of total phenols, flavonoids, tannins, alkaloids and steroids than the fruit extracts. Ethanolic extract in both fruits and leaves gave higher concentrations of phytochemical compounds than the ethyl acetate extracts. Therefore, fruit and leaves extract have antioxidant and antimicrobial activity against gram positive, negative bacteria and fungus. Also, the percentage of Liver cell line (HepG2), Colorectal adenocarcinoma (Caco-2) and Breast cell line (MCF-7) viability was decreased with increasing the concentrations of the ethanolic extract of fruits and leaves of Ficus sycomorus. The high concentrations of ethanolic extract of fruits caused high reduction in the viability of cancer cells, especially in Colorectal adenocarcinoma (Caco-2) cell line. In addition, phytochemical compound screened by GC-MS method. In GC-MS analysis, 12 bioactive phytochemical compounds were identified in fruits and 29 bioactive compounds were detected in leaves extract. These totally different active phytochemicals are found to possess a good vary of activities, which can facilitate within the protection against incurable diseases

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

A Survey on Retrieval of Mathematical Knowledge

We present a short survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 72 papers and tentative taxonomies of both retrieval problems and recurring techniques.Comment: CICM 2015, 20 page

Some entanglement features of three-atoms Tavis-Cummings model: Cooperative case

In this paper we consider a system of identical three two-level atoms interacting at resonance with a single-mode of the quantized field in a lossless cavity. The initial cavity field is prepared in the coherent state while the atoms are taken initially to be either in the uppermost excited state "$|eee>$" or The $\textmd{GHZ}$-state or the $\textmd{W}$-state. For this system we investigate different kinds of atomic inversion and entanglement, which arise between the different parts of the system due to the interaction. Also the relationship, between entanglement and some other nonclassical effects in the statistical properties, such as collapses and revivals in the atomic inversion where superharmonic effects appear, is discussed. The $Q$-functions for different cases are discussed. Most remarkably it is found that the $\textmd{GHZ}$-state is more robust against energy losses, showing almost coherent trapping and Schr\"odinger-cat states can not be produced from such state. Also the entanglement of $\textmd{GHZ}$-state is more robust than the $\textmd{W}$-state. Another interesting feature found is that the state which has no pairwise entanglement initially will have a much improvement of such pairwise entanglement through the evolution. Sudden death and sudden revival of atoms-pairwise entanglement are produced with the $\textmd{W}$-state.Comment: 14 pages, 7 figure

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