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This text was generated using a large language model, and select text has been reviewed and moderated for purposes such as readability.

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Math 201 Chapter 1 , Assignment #1-Solution 1.1 Exercises

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Jonathan Borwein

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Ali asghar Khoramshahi

Solve two mathematical puzzle simultaneously Fermat's last theorem and Andrew Beal's conjecture The last part of the issue Pierre de Fermat's, 1665AD Problem Fermat's: "It is impossible to have a sum of two cube numbers of one cube if all integers are greater than two" or: 1-1) The first method is proof: These First1th three answers are the reason why there is no answer for Fermat's because you are not equal: "xab≠xbc≠xac"

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Current lack of consensus on how to date or even classify " Late Neolithic " or " Early " or " Middle Chalcolithic " assemblages in the southern Levant is due not only to a past shortage of radiocarbon evidence but to misapplication of such evidence as we have an inconsistency in terminology. This paper presents some typological analyses of several assemblages with claimed " Wadi Rabah " and " Middle Chalcolithic " affinities as well as Bayesian analyses of the associated radiocarbon evidence. The results indicate that a group of assemblages with most of the characteristics we might consider most typical of Wadi Rabah date to the period 5800-5200 cal. BC. Some of the assemblages with this claim, however, fit neither the typological nor the chronological characteristics of Wadi Rabah, and appear to belong to a later, yet Pre-Ghassulian, Chalcolithic. Résumé : L'absence de consensus sur la manière de dater ou même de classifier les assemblages « Néolithique récent », « Chalcolithique ancien » ou « moyen » au Levant Sud est non seulement causée par le faible nombre de datations radiocarbones disponibles mais aussi par le mauvais usage qu'il en est fait, et par des incohérences quant à la terminologie. Cet article présente les analyses typologiques de plusieurs assemblages offrant des affinités dites « Wadi Rabah » et « Chalcolithique moyen » accompagnées d'analyses bayesiennes des dates radiocarbones qui leur sont associées. Les résultats obtenus montrent qu'un groupe de ces assemblages présentant la plupart des traits que l'on peut considérer comme les plus caractéristiques du « Wadi Rabah » daterait de 5800-5200 cal. BC. Toutefois, d'autres assemblages se réclamant aussi de Wadi Rabah ne nous semblent répondre ni aux caractères typologiques, ni à la place qu'occupe Wadi Rabah dans la séquence chronologique ; ils appartiendraient à un chalcolithique plus tardif, encore pré-ghassoulien.

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We present a formalism that sums up both soft-virtual (SV) and next to SV (NSV) contributions to all orders in perturbative QCD for the rapidity distribution of any colorless particle produced in hadron colliders. We have exploited the factorization properties and the renormalisation group (RG) invariance of the differential cross-section to achieve this. Using the state-of-the-art multiloop and multileg results, we determine the complete NSV contributions to third order in strong coupling constant for the rapidity distributions for a pair of leptons in Drell-Yan and also for Higgs boson in gluon fusion as well as bottom quark annihilation. Using the integral representation of our all order z space result, we show how the NSV contributions can be resummed in two-dimensional Mellin space.

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To ascertain the nasal bioavailability of Levonorgestrel and change formulation components to provide long-term effective concentrations of the drug in blood. An experimental study was conducted on rats to reduce dose and/or frequency of drug administration to reduce expected side effects reported in humans.In vivo study in rats.Centre of Relevance & Excellence in new drug delivery systems, Pharmacy Dept., G.H. Patel Budg., Faculty of Technology and Engineering, M.S. University of Baruda, Fatehgunj, Vadodara, Gujarat, India.Rats of proven fertility.Formulations containing 10-μg of levonorgestrel were administered in rats via the nasal route. Similarly, a 10-μg drug suspension was administered orally. The influence of the mucoadhesive agents chitosan and carbopol 934p on nasal absorption of the drug was also evaluated.Plasma drug concentration and pharmacokinetics.Relative bioavailabilities of 29.93%, 32.14%, and 25.97% were observed after nasal administration of plain drug, physical mixture, and liposomal formulations, respectively. Mucoadhesive agents in nasal formulations were found to produce a threefold increase in drug bioavailability. Bioavailability was improved from 29.93% to 101.70% and 99.42%, respectively, for chitosan (0.5%) and carbopol 934p (0.5%) formulations, with a significantly improved plasma half life from 7.0 hours to 55.7 hours and 52.9 hours, respectively. Pharmacodynamic studies indicate that the dosing interval can be changed from daily oral administration to nasal administration once every 2 days without changing the dose.Levonorgestrel with mucoadhesive agents administered nasally in rats is superior for maintaining effective drug concentrations over an extended period of time when compared with the presently available orally administered form.

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The relationship of vasculogenic mimicry to pigment in nodular vertical growth phase [VGP] cutaneous melanomas is assessed in this study. 10 nodules each from 27 tumors, 15 pigmented and 12 amelanotic were sampled in proportion to the pigment level. Serial frozen and paraffin sections subjected to HE, Reticulin, PAS to assess the vascular pattern; Dopa Oxidase and Immunopositivity for HMB45, LN5 [laminin 5] & integrin[α5β1], and EM [electron microscopy] to identify Weibel-Palade bodies within endothelial cells. The vascular pattern, pigment and the immunopositivity was mapped to assess the percentage VM [vasculogenic sinusoids] vs INC [incorporated microvasculature]. In pigmented melanomas, INC from pre-existing stromal vessels is predominant. Amelanotic melanomas show embryonic vasculogenic mimicry, a self-propagating system of spaces within the sheets of tumors cells. Both INC and VM co-exist in tumors with both amelanotic and melanotic nodules. In areas with VM, loci of LN5 and α5β1 integrin positive cells appear within the proliferating columns, positivity in these cells suggesting a switch to a more aggressive form. Irregular spaces appear lined by tumor cells, with initial hemopoeitic activity, coalesce and interlink into tubular networks. Spaces lined by tumor cells extend into an intricate network which then connects with the angiogenetic system. The tumor cells lining the vasculogenic spaces are positive for LN5, α5β1 integrin. Statistically, INC is significantly higher in pigmented melanomas, whereas amelanotic melanomas show significantly higher VM. Pigmentation is correlated positively with INC and negatively with VM. INC and VM are negatively correlated with each other.

ijeoma ikeji

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Increasing consumer demand for natural products have renewed food industry attention in bio preservation. Lactic acid bacteria are of particular interest as effective alternative to chemical preservation because of their food grade status. This work explores the effect of antifungal compounds produced by isolates of Lactobacillus sp on some selected pathogenic fungi growth. Samples of diary and fermented products were purchased from commercial vendors within the Federal Capital Territory (FCT) and screened for the presence of Lactobacillus sp. The Lactobacillus sp isolated were screened for antifungal activity against Aspergillus fumigatus, Candida albicans and Trichophyton rubrum using a dual culture assay. Strains with antifungal activity were identified and the fungal inhibitory activity was further evaluated. The effect of abiotic factors on the antifungal activity was evaluated by overlay assay under different temperature and pH. Majority of the identified isolates belonged to ...

sakshi choudhary

2016, Asian Journal of Oncology

Objective: The objective of this study was to assess a correlation between tumor volume, the spread and metastatic potential of the tumor. Materials and Methods: A prospective study was done on 40 cases of carcinoma of cervix with stage IIb or less. The hysterectomy specimens alongwith the lymph nodes were sent to the histopathology department. Clinical details were taken from gynecology department. Hematoxylin and eosin slides were prepared and seen. Tumor volume was calculated by using the formula TV = π/6×Length×Width×Depth. Immunohistochemistry for Fibronectin and LN5 was also done. Results: The median age of the patients in this group was 47.5 years, with a range of 30–80 years. The major histological type of carcinoma among 40 cases is squamous cell carcinoma (SCC) (in 90% of cases), and 10% had adenocarcinoma. Pathological staging of the carcinoma cervix showed stage Ib, IIa, IIb, and IVa (35%, 20%, 40%, and 5%). Tumor volume estimated on pathological specimens of 40 cases ra...

2011, Silva Fennica

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