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

Modulational instability of ion-acoustic wave packets in quantum pair-ion plasmas

Amplitude modulation of quantum ion-acoustic waves (QIAWs) in a quantum electron-pair-ion plasma is studied. It is shown that the quantum coupling parameter $H$ (being the ratio of the plasmonic energy density to the Fermi energy) is ultimate responsible for the modulational stability of QIAW packets, without which the wave becomes modulational unstable. New regimes for the modulational stability (MS) and instability (MI) are obtained in terms of $H$ and the positive to negative ion density ratio $\beta$. The growth rate of MI is obtained, the maximum value of which increases with $\beta$ and decreases with $H$. The results could be important for understanding the origin of modulated QIAW packets in the environments of dense astrophysical objects, laboratory negative ion plasmas as well as for the next generation laser solid density plasma experiments.Comment: 4 pages, 2 figures (to appear in Astrophysics and Space Science

Serial production line performance under random variation:Dealing with the ‘Law of Variability’

Many Queueing Theory and Production Management studies have investigated specific effects of variability on the performance of serial lines since variability has a significant impact on performance. To date, there has been no single summary source of the most relevant research results concerned with variability, particularly as they relate to the need to better understand the ‘Law of Variability’. This paper fills this gap and provides readers the foundational knowledge needed to develop intuition and insights on the complexities of stochastic simple serial lines, and serves as a guide to better understand and manage the effects of variability and design factors related to improving serial production line performance, i.e. throughput, inter-departure time and flow time, under random variation

Nonlinear structures: explosive, soliton and shock in a quantum electron-positron-ion magnetoplasma

Theoretical and numerical studies are performed for the nonlinear structures (explosive, solitons and shock) in quantum electron-positron-ion magnetoplasmas. For this purpose, the reductive perturbation method is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining extended quantum Zakharov-Kuznetsov equation. The latter has been solved using the generalized expansion method to obtain a set of analytical solutions, which reflect the possibility of the propagation of various nonlinear structures. The relevance of the present investigation to the white dwarfs is highlighted.Comment: 7 figure

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

Mitochondrial DNA depletion syndrome presenting with ataxia and external ophthalmoplegia: Case report

The mitochondrial DNA depletion syndromes are autosomal recessive disorders characterized by decreased mitochondrial DNA copy number in affected tissues.Mutations in 2 genes involved in deoxyribonucleotide metabolism, the deoxyguanosine kinase gene and the thymidine kinase 2 gene, had been related to this syndrome. This study aims to describe the clinical, histochemical, biochemical and molecular diagnosis of one Egyptian pediatric patient with the myopathic form of mitochondrial depletion syndrome. The patient presented to Cairo University Pediatric Hospital with the clinical suspicion of mitochondrial encephalomyopathy. Histochemical and biochemical studies of the respiratory chain complexes were performed on the muscle biopsy specimen from the patient. Molecular diagnosis was done by quantitative radioactive Southern blot and sequencing analysis of the whole coding regions of the TK2 gene. Histochemical staining revealed cytochrome oxidase negative fibers and increased staining for succinate dehydrogenase. The activity of complex I was not detected and complex IV activity was about 46%of age matched controls. Southern blot analysis showed reduction of the mitochondrial/nuclear DNA ratio, the degree of depletion was around 30% of aged-matched controls. Sequencing analysis of the TK2 gene revealed no sequence variation. Targeted molecular diagnosis based on the biochemical analysis of the respiratory chain enzymes makes the molecular evaluation of mitochondrial disorders much easier. Involvement of other nuclear genes rather than TK2 gene in the pathogenesis of the myopathic form of mitochondrial depletion syndrome should be considered.Keywords: Mitochondrial; Nuclear; Sequencing; Depletion; Mutation

Diethyl 3,4-dimethylthieno[2,3-it b]thiophene-2,5-dicarboxylate

In the title compound, C14H16O4S2, the thieno[2,3-b]thiophene ring systems are planar [maximum deviation = 0.008 (2) Å]. The molecular conformation is stabilized by intramolecular C-HO hydrogen bonds, while the crystal packing is stabilized by C-HO, C-H and - stacking [centroid-centroid distance = 3.6605 (14) Å] interactions, which lead to supramolecular layers in the ab plane

USE THE DRIS METHOD TO DETERMINE THE BEST NUTRIENTS BALANCE FOR CHICKPEA PLANTS THROUGH THE RELATIONSHIP BETWEEN NORMS AND CRITICAL POINT RATE

This study was aimed to determine the best nutrient balance for chickpeas from the relationship between the Norms of nutrients with the critical point for each nutrient using the DRIS system. This experiment was carried out at the Grdarasha farm, college of Agriculture Engineering Science, University of Salahaddin during the spring growing season of 2020, to find out the effects of three levels of nitrogen (UREA) (0, 15, 30 Kg N ha-1), four levels of triple super phosphate (0, 20, 40, 60 Kg P ha-1), and three levels of KCl fertilizer (0, 15, 30 Kg K ha-1) and their combination on Chickpea yield and nutrient balance by using Split Split plot design with three replicates. The highest yield (1.55 Mg ha-1) was recorded from the lowest (2.02) AT or NBI (nutrient balance index), while the lowest yield (0.73 Mg ha-1) was obtained from the highest AT value (62.68)

Mouth Function Determines The Shape Oscillation Pattern In Regenerating Hydra Tissue Spheres

Hydra is a small freshwater polyp capable of regeneration from small tissue pieces and from aggregates of cells. During regeneration, a hollow bilayered sphere is formed that undergoes osmotically driven shape oscillations of inflation and rupture. These oscillations are necessary for successful regeneration. Eventually, the oscillating sphere breaks rotational symmetry along the future head-foot axis of the animal. Notably, the shape oscillations show an abrupt shift from large-amplitude, long-period oscillations to small-amplitude, short-period oscillations. It has been widely accepted that this shift in oscillation pattern is linked to symmetry breaking and axis formation, and current theoretical models of Hydra symmetry breaking use this assumption as a model constraint. However, a mechanistic explanation for the shift in oscillation pattern is lacking. Using in vivo manipulation and imaging, we quantified the shape oscillation dynamics and dissected the timing and triggers of the pattern shift. Our experiments demonstrate that the shift in the shape oscillation pattern in regenerating Hydra tissue pieces is caused by the formation of a functional mouth and not by shape symmetry breaking as previously assumed. Thus, model assumptions must be revised in light of these new experimental data, which can be used to constrain and validate improved theoretical models of pattern formation in Hydra