Geometry of Discrete Quantum Computing

Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2^{n} infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields Fp^2 (based on primes p congruent to 3 mod{4}) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space CP{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p+1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to DCP{2^{n}-1}, the discrete analog of the complex projective space, which has p^{2^{n}-1} (p-1)\prod_{k=1}^{n-1} (p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field Fp^2 have p^{n} (p-1)^{n} unentangled states (the product of the tally for a single qubit) with purity 1, and they have p^{n+1}(p-1)(p+1)^{n-1} maximally entangled states with purity zero.Comment: 24 page

Risks of Environmental Genotoxicants

Humans have throughout their development been exposed to various environmental genotoxicants through food, air, water, and soil. Environmental exposure to genotoxic compounds may induce damage to human health and thereby increase risks of human cancers and other diseases. Environmental genotoxic chemicals have the ability to induce mutations. Such mutations can give rise to cancer in somatic cells. However, when germ cells are affected, the damage can also have an effect on the next and successive generations. Because of the potential health hazard represented by exposure to genotoxic chemicals, it is important that all chemicals for which there is possible human exposure be screened for genotoxic activity. If genotoxic hazard is detected, then the risks of exposure can be assessed and the use of the chemical controlled and when appropriate eliminated from the market and the environment. In this chapter, a general overview of the genotoxicity and the genotoxicity of some environmental genotoxicants are discussed. This is followed by a description of the genotoxic properties of some environmental genotoxicants such as bisphenols and mycotoxins, which are prominent environmental contaminates, and is believed to be genotoxic agents that contribute to the high incidence of carcinogenicity among populations

Solitary and blow-up electrostatic excitations in rotating magnetized electron-positron-ion plasmas

The nonlinear dynamics of a rotating magnetoplasma consisting of electrons, positrons and stationary positive ions is considered. The basic set of hydrodynamic and Poisson equations are reduced to a Zakharov-Kuznetsov (ZK) equation for the electric potential. The ZK equation is solved by applying an improved modified extended tanh-function method (2008 Phys. Lett. A 372 5691) and its characteristics are investigated. A set of new solutions are derived, including localized solitary waves, periodic nonlinear waveforms and divergent (explosive) pulses. The characteristics of these nonlinear excitations are investigated in detail

Natural Cholesterol Busters

Hypercholesterolemia, a risk factor for cardiovascular and cerebrovascular diseases, is a silent health problem. It occurs due to buildup of large amount of cholesterol in blood vessels resulting in narrowed blood vessels or blockage of the flow of blood and causes cellular dysfunction. The predisposing factors for hypercholesterolemia are carbohydrates‐enriched diet, unhealthy fats, and red meat. Moreover, family history, obesity, hypokinetic lifestyle, aging, and oxidative stress are associated with hypercholesterolemia. Therapeutic interventions of hypercholesterolemia involve cessation of bad habits, regular exercise, consumption of cholesterol buster diets, and cholesterol‐lowering drugs. However, cholesterol‐lowering drugs have low efficacy, and some patients cannot tolerate the adverse effects of hypocholesterolemic drugs. In light of this, there has been great interest to address natural cholesterol busters as first choice as cholesterol‐lowering option. Healthy diet, regular exercise and natural cholesterol‐lowering agents are documented to decrease blood cholesterol level. Natural cholesterol busters include dietary fibers, plant sterols, healthy fats, smart proteins, antinutrients, antioxidants, and L‐arginine. These busters not only decrease cholesterol oxidation and absorption but also increase cholesterol catabolism and elimination. Most of these busters are found in cereals, oatmeal, fruits, vegetables, legumes, and fermented foods. The natural cholesterol busters are recommended strategies for treatment of hypercholesterolemia alone or in combination with cholesterol‐lowering drugs

Ceftriaxone as an Inhibitor for Corrosion of Al in Formic Acid Solutions

The inhibiting effect of ceftriaxone on the corrosion of Al in HCOOH solution was studied by means of weight loss, thermometry, hydrogen evolution and potentiodynamic polarization techniques, complemented with surface examination using scanning electron microscopy (SEM). The obtained results showed that ceftriaxone are excellent inhibitor in HCOOH solution. The inhibition efficiency increases with inhibitor concentration. Polarization curves indicate that ceftriaxone was acted as a mixed-type inhibitor. The adsorption of the inhibitor on Al surface was found to obey Langmuir isotherm and showed a physisorption mechanism. The thermodynamic activation and adsorption parameters were calculated and discussed. Keywords: Ceftriaxone, aluminum, corrosion inhibitor, potentiodynamic polarization, adsorption, gravimetry and gasometr

Effects of administration of 10 nm or 50 nm gold nanoparticles (AuNPs) on blood profile, liver and kidney functions in male albino rats

This work aimed to investigate the effect of acute and chronic administration of gold nanoparticles (GNPs) on liver and kidney functions, blood glucose concentration, lipid profile, and haematological parameters in male albino rats. Two experiments were conducted. In acute study: Fifty-four adult mature male rats were randomly assigned into three equal groups (18 per group). Group 1 (control group): in which rats were received intramuscular (i.m) injection of 1 ml normal saline 0.9%. Group 2 (50 nm GNPs group): rats were i.m. injected with a single dose of 75 µg 50 nm GNPs/kg body weight (bwt). In Group 3 (10 nm GNPs group): rats were i.m. injected with a single dose of 75 µg 10 nm GNPs/kg bwt. In chronic study: Eighteen adult male rats were randomly divided into three equal groups (6 per group). Group І (control): rats were intramuscular (i.m) repeatedly injected with 1 ml normal saline 0.9% once/week 5 for weeks. Group 2 (50 nm GNPs): rats were i.m. injected with once/week with a dose of 75 µg 50 nm GNPs/kg bwt) for 5 weeks. In Group 3 (10 nm GNPs): male rats were i.m. injected with once/week with a dose of 75 µg 50 nm GNPs/kg bwt for 5 weeks, followed by 3 weeks washout period for all groups. Blood was collected at 3, 7, and 60 days in acute experiment, while, they were collected only before and after 2 months in chronic experiment. Acute and chronic administration of GNPs (10 or 50 nm size) in male albino rats induced no significant alterations for liver and kidney functions, lipid profile parameters and different haematological parameters at days 3 and 60 of the study. However, on day-7 post-treatment, GNPs-treated rats showed significantly (P <0.05) higher serum ALT, AST, ALP, urea, creatinine, glucose, and different lipid profile and decreased HDL level. Chronic administration of 10 nm or 50 nm GNPs significantly (P <0.05) decreased serum glucose levels. In conclusion acute or chronic administration of 10 nm or 50 nm GNPs could alter the liver, kidney functions and blood profile on day 7 post-treatment, however, these values returned to the normal levels on day 60 post- injection. Also, the chronic administration of GNPs induced a hypoglycemic effect in male albino rats

Towards a canonical classical natural deduction system

This paper studies a new classical natural deduction system, presented as a typed calculus named \lml. It is designed to be isomorphic to Curien-Herbelin's calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is a combination of Parigot's $\lambda\mu$-calculus with the idea of ``coercion calculus'' due to Cervesato-Pfenning, accommodating let-expressions in a surprising way: they expand Parigot's syntactic class of named terms. This calculus aims to be the simultaneous answer to three problems. The first problem is the lack of a canonical natural deduction system for classical logic. \lml is not yet another classical calculus, but rather a canonical reflection in natural deduction of the impeccable treatment of classical logic by sequent calculus. The second problem is the lack of a formalization of the usual semantics of Curien-Herbelin's calculus, that explains co-terms and cuts as, respectively, contexts and hole-filling instructions. The mentioned isomorphism is the required formalization, based on the precise notions of context and hole-expression offered by \lml. The third problem is the lack of a robust process of ``read-back'' into natural deduction syntax of calculi in the sequent calculus format, that affects mainly the recent proof-theoretic efforts of derivation of $\lambda$-calculi for call-by-value. An isomorphic counterpart to the $Q$-subsystem of Curien-Herbelin's-calculus is derived, obtaining a new $\lambda$-calculus for call-by-value, combining control and let-expressions.Fundação para a Ciência e a Tecnologia (FCT