ANDY BEAL’S CONJECTURE ( PART1 AND PART 2)

This paper provides an algebraic mathematical proof to the below and proves their validity. 1)     The Andy Beal’s conjecture 2)     The Fermats last theorem 3)     The Wells summation conjecture 4)     The Goldbach conjecture 5)     The existence of  solitary numbers eg -10 Keywords: conjecture, vector analysis, three dimension, two dimension, increment, complex, law of algebra, prime factor, domain, algorithm, input, integer, real number line, dual set, magnitude, resultant, compute, binary, hack, twelve, shrink, standard, probability, linear equation, intersect, finite, 2% logarithmic, surds, narrow range, 98%, one dimensional space, compare, determine, flow, generalization,  infinity, independent, error, constant (k), dependent, graph, discretely, unaffected, HSIV, 4-input synchronous tetra- set, S4ISC, frequency, per binary input (BPI), aeroplane, run way, air friction, air resistance, take off angle,  plane crash, geometry, optimum, slope, partially collapsed, totally collapsed, supremacy, incoherence, airflight study, name, equation index or factor, honour, constant factor, economics, start discontinuity, man, robot, creation, simultaneously, cage theory, like energies

BEAL’S CONJECTURE

This paper provides algebraic mathematical proof to 6 unsolved problems in mathematics (number theory) and 3 others. 1)       The Beal’s conjecture (invalid forever) 2)       The Wells summation theorem 3)       The Fermats last theorem (376yrs- invalid forever) 4)       Unification engine of  all Power  summations 5)       The Goldbach conjecture (271yrs-valid forever) 6)       The proof of solitary -10-(valid forever ) 7)       NP VS P-problem,[ANS=NP≠P =[ NP- UNTIL- P ]= [NP-R-EI-T-P] 8)       The Riemann Hypothesis (invalid forever) 9)       Power summation pyramid-Carnox pyramid Keywords: conjecture, vector analysis, three dimension, two dimension, increment, complex, law of algebra, prime factor, domain, algorithm, input, integer, real number line, dual set, magnitude, resultant, compute, binary, hack, twelve, shrink, standard, probability, linear equation, intersect, finite, 2% logarithmic, surds, narrow range, 98%, one dimensional space, compare, determine, flow, generalization,  infinity, independent, error, constant (k), dependent, graph, discretely, unaffected, HSIV, 4-input synchronous tetra- set, S4ISC, frequency, per binary input (BPI), aeroplane, run way, air friction, air resistance, take off angle, plane crash, geometry, optimum, slope, partially collapsed, totally collapsed, supremacy, incoherence, airflight study, name, equation index or factor, honour, constant factor, economics, start discontinuity, man, robot, creation, simultaneously, cage theory, like energies, function solute, trivial, non-trivial, unplu

Immunization expands B cells specific to HIV-1 V3 glycan in mice and macaques.

Broadly neutralizing monoclonal antibodies protect against infection with HIV-1 in animal models, suggesting that a vaccine that elicits these antibodies would be protective in humans. However, it has not yet been possible to induce adequate serological responses by vaccination. Here, to activate B cells that express precursors of broadly neutralizing antibodies within polyclonal repertoires, we developed an immunogen, RC1, that facilitates the recognition of the variable loop 3 (V3)-glycan patch on the envelope protein of HIV-1. RC1 conceals non-conserved immunodominant regions by the addition of glycans and/or multimerization on virus-like particles. Immunization of mice, rabbits and rhesus macaques with RC1 elicited serological responses that targeted the V3-glycan patch. Antibody cloning and cryo-electron microscopy structures of antibody-envelope complexes confirmed that immunization with RC1 expands clones of B cells that carry the anti-V3-glycan patch antibodies, which resemble precursors of human broadly neutralizing antibodies. Thus, RC1 may be a suitable priming immunogen for sequential vaccination strategies in the context of polyclonal repertoires

Green's Function Monte Carlo for Lattice Fermions: Application to the t-J Model

We develop a general numerical method to study the zero temperature properties of strongly correlated electron models on large lattices. The technique, which resembles Green's Function Monte Carlo, projects the ground state component from a trial wave function with no approximations. We use this method to determine the phase diagram of the two-dimensional t-J model, using the Maxwell construction to investigate electronic phase separation. The shell effects of fermions on finite-sized periodic lattices are minimized by keeping the number of electrons fixed at a closed-shell configuration and varying the size of the lattice. Results obtained for various electron numbers corresponding to different closed-shells indicate that the finite-size effects in our calculation are small. For any value of interaction strength, we find that there is always a value of the electron density above which the system can lower its energy by forming a two-component phase separated state. Our results are compared with other calculations on the t-J model. We find that the most accurate results are consistent with phase separation at all interaction strengths.Comment: 22 pages, 22 figure

Hole Doping Evolution of the Quasiparticle Band in Models of Strongly Correlated Electrons for the High-T_c Cuprates

Quantum Monte Carlo (QMC) and Maximum Entropy (ME) techniques are used to study the spectral function $A({\bf p},\omega)$ of the one band Hubbard model in strong coupling including a next-nearest-neighbor electronic hopping with amplitude $t'/t= -0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for $Sr_2 Cu O_2 Cl_2$. A narrow quasiparticle (q.p.) band is observed in the QMC analysis at the temperature of the simulation $T=t/3$, both at and away from half-filling. Such a narrow band produces a large accumulation of weight in the density of states at the top of the valence band. As the electronic density $$ decreases further away from half-filling, the chemical potential travels through this energy window with a large number of states, and by $\sim 0.70$ it has crossed it entirely. The region near momentum $(0,\pi)$ and $(\pi,0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from $(0,0)$ to $(\pi,\pi)$. The evolution with hole density of the quasiparticle dispersion contains some of the features observed in recent ARPES data in the underdoped regime. For sufficiently large hole densities the ``flat'' bands at $(\pi,0)$ cross the Fermi energy, a prediction that could be tested with ARPES techniques applied to overdoped cuprates. The population of the q.p. band introduces a {\it hidden} density in the system which produces interesting consequences when the quasiparticles are assumed to interact through antiferromagnetic fluctuations and studied with the BCS gap equation formalism. In particular, a region of extended s-wave is found to compete with d-wave in the overdoped regime, i.e. when the chemical potential has almost entirely crossed the q.p.Comment: 14 pages, Revtex, with 13 embedded ps figures, submitted to Phys. Rev. B., minor modifications in the text and in figures 1b, 2b, 3b, 4b, and 6

Reshaping Curriculum to Enhance the Relevance of Literary Competence in Children's Education06

Twenty-first century learners face a multi-literacy landscape as they strive to acquire the cognitive skills needed for independent learning, apply linguistic skills to other knowledge base, and become computer literate. This article envisions a combination of skill sets and knowledge bases as the foundation of a literary competence-based curriculum. Such a curriculum would have the goal of enhancing young learners"critical thinking abilities; this would also help them take charge of the cognitive,linguistic, and sociocultural dimensions of written and spoken language in order to make learning transferable and applicable to the real world

Measurement of Rb in e+e- Collisions at 182 - 209 GeV

Measurements of Rb, the ratio of the bbbar cross-section to the qqbar cross- section in e+e- collisions, are presented. The data were collected by the OPAL experiment at LEP at centre-of-mass energies between 182 GeV and 209 GeV. Lepton, lifetime and event shape information is used to tag events containing b quarks with high efficiency. The data are compatible with the Standard Model expectation. The mean ratio of the eight measurements reported here to the Standard Model prediction is 1.055+-0.031+-0.037, where the first error is statistical and the second systematic.Comment: 21 pages, 5 figures, Submitted to Phys. Letts

Measurement of the partial widths of the Z into up- and down-type quarks

Using the entire OPAL LEP1 on-peak Z hadronic decay sample, Z -> qbarq gamma decays were selected by tagging hadronic final states with isolated photon candidates in the electromagnetic calorimeter. Combining the measured rates of Z -> qbarq gamma decays with the total rate of hadronic Z decays permits the simultaneous determination of the widths of the Z into up- and down-type quarks. The values obtained, with total errors, were Gamma u = 300 ^{+19}_{-18} MeV and Gamma d = 381 ^{+12}_{-12} MeV. The results are in good agreement with the Standard Model expectation.Comment: 22 pages, 5 figures, Submitted to Phys. Letts.

Large-scale genome-wide association studies and meta-analyses of longitudinal change in adult lung function.

BACKGROUND: Genome-wide association studies (GWAS) have identified numerous loci influencing cross-sectional lung function, but less is known about genes influencing longitudinal change in lung function. METHODS: We performed GWAS of the rate of change in forced expiratory volume in the first second (FEV1) in 14 longitudinal, population-based cohort studies comprising 27,249 adults of European ancestry using linear mixed effects model and combined cohort-specific results using fixed effect meta-analysis to identify novel genetic loci associated with longitudinal change in lung function. Gene expression analyses were subsequently performed for identified genetic loci. As a secondary aim, we estimated the mean rate of decline in FEV1 by smoking pattern, irrespective of genotypes, across these 14 studies using meta-analysis. RESULTS: The overall meta-analysis produced suggestive evidence for association at the novel IL16/STARD5/TMC3 locus on chromosome 15 (P  =  5.71 × 10(-7)). In addition, meta-analysis using the five cohorts with ≥3 FEV1 measurements per participant identified the novel ME3 locus on chromosome 11 (P  =  2.18 × 10(-8)) at genome-wide significance. Neither locus was associated with FEV1 decline in two additional cohort studies. We confirmed gene expression of IL16, STARD5, and ME3 in multiple lung tissues. Publicly available microarray data confirmed differential expression of all three genes in lung samples from COPD patients compared with controls. Irrespective of genotypes, the combined estimate for FEV1 decline was 26.9, 29.2 and 35.7 mL/year in never, former, and persistent smokers, respectively. CONCLUSIONS: In this large-scale GWAS, we identified two novel genetic loci in association with the rate of change in FEV1 that harbor candidate genes with biologically plausible functional links to lung function

A measurement of the tau mass and the first CPT test with tau leptons

We measure the mass of the tau lepton to be 1775.1+-1.6(stat)+-1.0(syst.) MeV using tau pairs from Z0 decays. To test CPT invariance we compare the masses of the positively and negatively charged tau leptons. The relative mass difference is found to be smaller than 3.0 10^-3 at the 90% confidence level.Comment: 10 pages, 4 figures, Submitted to Phys. Letts.