Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

MSC 2010: 30C10, 32A30, 30G35The algebra R(1; j; j2; j3), j4 = ¡1 of the fourth-R numbers, or in other words the algebra of the double-complex numbers C(1; j) and the corresponding functions, were studied in the papers of S. Dimiev and al. (see [1], [2], [3], [4]). The hyperbolic fourth-R numbers form other similar to C(1; j) algebra with zero divisors. In this note the square roots of hyperbolic fourth-R numbers and hyperbolic complex numbers are found. The quadratic equation with hyperbolic fourth-R coefficients and variables is solved. The Cauchy-Riemann system for holomorphicity of fourth-R functions is recalled. Holomorphic homogeneous polynomials of fourth-R variables are listed

Hyperbolic Double-Complex Laplace Operator

2010 Mathematics Subject Classification: 35G35, 32A30, 30G35.In this paper is introduced the hyperbolic double-complex Laplace operator. The hyperbolic decomplexification of the hyperbolic doublecomplex Laplace operator and its characteristic set is found. The exponential eigenfunctions of the zero eigenvalue of the hyperbolic double-complex Laplace operator are found as well

Proton pump inhibitors display antitumor effects in barrett's adenocarcinoma cells

Recent evidence has reported that proton pump inhibitors (PPIs) can exert antineoplastic effects through the disruption of pH homeostasis by inhibiting vacuolar ATPase (H+-VATPase), a proton pump overexpressed in several tumor cells, but this aspect has not been deeply investigated in EAC yet. In the present study, the expression of H+-VATPase was assessed through the metaplasia-dysplasia-adenocarcinoma sequence in Barrett''s esophagus (BE) and the antineoplastic effects of PPIs and cellular mechanisms involved were evaluated in vitro. H+-VATPase expression was assessed by immunohistochemistry in paraffined-embedded samples or by immunofluorescence in cultured BE and EAC cell lines. Cells were treated with different concentrations of PPIs and parameters of citotoxicity, oxidative stress, and autophagy were evaluated. H+-VATPase expression was found in all biopsies and cell lines evaluated, showing differences in the location of the pump between the cell lines. Esomeprazole inhibited proliferation and cell invasion and induced apoptosis of EAC cells. Production of reactive oxygen species (ROS) seemed to be involved in the cytotoxic effects observed since the addition of N-acetylcysteine significantly reduced esomeprazole-induced apoptosis in EAC cells. Esomeprazole also reduced intracellular pH of tumor cells, whereas only disturbed the mitochondrial membrane potential in OE33 cells. Esomeprazole induced autophagy in both EAC cells, but also triggered a blockade in autophagic flux in the metastatic cell line. These data provide in vitro evidence supporting the potential use of PPIs as novel antineoplastic drugs for EAC and also shed some light on the mechanisms that trigger PPIs cytotoxic effects, which differ upon the cell line evaluated

Denatonium benzoate decreases the effect of histamine in vitro and in rats

Purpose: To evaluate the effect of denatonium benzoate (DB) in histamine-induced model of inflammation and the effect of the selective H1 receptor agonist (2-(2-Pyridyl) ethylamine) on rat gastric smooth muscle strips pretreated with DB.Methods: The anti-inflammatory effect of DB was evaluated in vivo on histamine-induced rat paw edema. In vitro studies on spontaneous muscle contraction were performed on smooth muscle strips isolated from rat gastric corpus.Results: The results showed a well-defined anti-inflammatory effect of DB (15 mg/kg) during the early stage of rat paw edema at the 15th (p < 0.001), 30th (p < 0.01) and 60th min (p < 0.001) compared to control. In vitro experiments indicated reduced spontaneous contractile activity of smooth muscle strips to H1 receptor agonist in the presence of DB (0.5 μM). The vascular effects of histamine are mediated by H1 receptors. Substances, which reduce the effect of histamine on the H1 receptors could influence the early stage of histamine-induced inflammation.Conclusion: The results show that the anti-inflammatory activity of DB probably is related to its antagonistic activity on histamine H1 receptors. The results would contribute to the search for new antiinflammatory drugs. Keywords: Denatonium benzoate, Inflammation, Histamine, Muscle contractio

Patient and caregiver assessment of the benefits from the clinical use of amyloid PET imaging

INTRODUCTION: Few studies to date have explored patient and caregiver views on the clinical use of amyloid positron emission tomography (PET). METHODS: A 7-item questionnaire assessing patient and caregiver views (510 total respondents) toward amyloid PET imaging was advertised broadly through alz.org/trialmatch. RESULTS: We received 510 unique responses from 48 US states, 2 Canadian provinces, the Dominican Republic, and Greece. Both patients and caregivers indicated that they would want to receive amyloid imaging if offered the opportunity. Over 88% of respondents had a positive response (∼10% with neutral and 2% with negative responses) to whether amyloid PET should be offered routinely and be reimbursed. Such information was felt to be useful for long-term legal, financial, and health care planning. Respondents identifying with early age cognitive decline (younger than 65 y) were more likely to explore options for disability insurance (P=0.03). Responders from the Midwest were more likely to utilize information from amyloid imaging for legal planning (P=0.02), disability insurance (P=0.02), and life insurance (P=0.04) than other US regions. DISCUSSION: Patients and caregivers supported the use of amyloid PET imaging in clinical practice and felt that the information would provide significant benefits particularly in terms of future planning

Widespread white matter and conduction defects in PSEN1-related spastic paraparesis

The mechanisms underlying PSEN1 mutation-associated spastic paraparesis (SP) are not clear. We compared diffusion and volumetric magnetic resonance measures between 3 persons with SP associated with the A431E mutation and 7 symptomatic persons with PSEN1 mutations without SP matched for symptom duration. We performed amyloid imaging and central motor and somatosensory conduction studies in one subject with SP. We found decreases in fractional anisotropy and increases in mean diffusivity in widespread white matter areas including the corpus callosum, occipital, parietal, and frontal lobes in PSEN1 mutation carriers with SP. Volumetric measures were not different and amyloid imaging showed low signal in sensorimotor cortex and other areas in a single subject with SP. Electrophysiological studies demonstrated both slowed motor and sensory conduction in the lower extremities in this same subject. Our results suggest that SP in carriers of the A431E PSEN1 mutation is a manifestation of widespread white matter abnormalities not confined to the corticospinal tract that is at most indirectly related to the mutation’s effect on APP processing and amyloid deposition

Бринзоламид/тимолол и латанопрост в лечении псевдоэксфолиативной глаукомы: сравнительное исследование

PURPOSE: To compare the long-term effectiveness of pseudoexfoliative glaucoma (PEG) treatment with a fixed combination (FC) brinzolamide/timolol vs. latanoprost by a comprehensive assessment of structural and functional changes, as well as indicators of arterial ocular blood flow. METHODS: We observed 42 patients with PEG who received FC brinzolamide/timolol (22 patients) 2 times daily or latanoprost once a day (20 patients). The groups were homogeneous for age (66.05±1.241 in brinzolamide/ timolol group and 63.8±2.09 in latanoprost group, p=0.36) and glaucoma stages (MD -6.43±1.51 dB in brinzolamide/ timolol group and -8.02±2.08 dB in latanoprost group, p=0.54), intraocular pressure (IOP) levels were also comparable (19.59±0.79 mm Hg in brinzolamide/timolol group and 19.94±0.88 mm Hg in latanoprost group, p=0.77). The functional and morphometric parameters, studied by means of standard automated perimetry and spectral optical coherence tomography, and ocular blood flow parameters, measured by color Doppler Imaging with impulse Doppler sonography, were subjected to a comparative evaluation. Follow up period was 10.5±0.363 month. RESULTS: A significant IOP reduction, compared with baseline was observed in both groups: 11% from baseline in brinzolamide/timolol group (p=0.005) and 12.5% from baseline in latanoprost group (p=0.011). MD was improved in brinzolamide/timolol group: by 1.2±0.37 dB (p=0.003). No statistically significant difference in RNFL, GlV and GCC was obtained in both groups during the follow up period. However, by the end of 12 months a significant increase of FLV was noted in latanoprost group (p=0.04). By the end of the observation period patients treated with brinzol-amide/timolol showed an increase in diastolic blood flow in the ophthalmic artery (p=0.044) and systolic blood flow in the lateral posterior short ciliary artery (p=0.011). CONCLUSION: FC brinzolamide/timolol and latanoprost demonstrate a significant hypotensive efficacy in PEG, however FC brinzolamide/timolol unlike latanoprost provides stabilization of glaucomatous optic neuropathy, as evidenced by the preservation of visual function and morpho-metric parameters of the retina and optic nerve, as well as an improved arterial ocular blood flow.ЦЕЛЬ. Сравнить долгосрочную эффективность лечения псевдоэксфолиативной глаукомы (ПЭГ) фиксированной комбинацией бринзоламид/тимолол (ФК бринзоламид/ тимолол) с латанопростом на основании комплексной оценки структурных и функциональных изменений, а также показателей артериального глазного кровотока. МЕТОДЫ. В исследовании приняли участие 42 пациента с ПЭГ, получавшие ФК бринзоламид/тимолол (22 больных) 2 раза в день или латанопрост 1 раз в день (20 больных). Группы были однородны по возрасту (66,05±1,24 года в группе, получавшей ФК бринзоламид/тимолол, и 63,8±2,09 года в группе, получавшей латанопрост, р=0,36), по стадиям глаукомы (MD -6,43±1,51 дБ в группе ФК бринзоламид/тимолол и -8,027±2,08 дБ в группе латанопрост, р=0,54), а также по исходному уровню внутриглазного давления (19,59±0,79 и 19,94±0,88 мм рт.ст. соответственно в группах ФК бринзоламид/тимолол и латанопрост, р=0,77). Сравнительной оценке подвергнуты функциональные и морфометрические показатели, полученные при стандартной автоматизированной периметрии и спектральной оптической когерентной томографии, а также параметры регионарной гемодинамики глаза, измеренные в динамике методом цветового доп-плеровского картирования с импульсной допплерогра-фией. Средний срок наблюдения составил 10,5±0,36 мес. РЕЗУЛЬТАТЫ. В обеих группах больных наблюдалось достоверное по сравнению с исходным снижение ВГД, которое составило в группе ФК бринзоламид/тимолол 11% от исходного (p=0,005) и в группе латанопрост 12,5% от исходного (p=0,011). Было отмечено улучшение периметрического индекса MD у больных, получавших ФК бринзоламид/тимолол, на 1,2±0,37 дБ по сравнению с исходным (p=0,003). Статистически значимого изменения морфометрических показателей в динамике не было отмечено ни в одной группе, за исключением достоверного увеличения индекса FLV (p=0,04) у больных, получавших латанопрост. У пациентов, лечившихся ФК бринзоламид/тимолол, к концу наблюдения отмечено увеличение диастолической скорости кровотока в глазной артерии (p=0,044) и систолической скорости кровотока в латеральной задней короткой цилиарной артерии (p=0,011). ЗАКЛЮЧЕНИЕ. ФК бринзоламид/тимолол и латанопрост обладают выраженной гипотензивной эффективностью в лечении ПЭГ, однако ФК бринзоламид/тимолол, но не латанопрост, обеспечивает стабилизацию глаукомной оптической нейропатии, о чем свидетельствует сохранение зрительных функций и морфометрических характеристик сетчатки и зрительного нерва, а также улучшение артериального глазного кровотока

Testing Influences of APOE and BDNF Genes and Heart Failure on Cognitive Function

Background Apolipoprotein E ( APOE) ε2, ε4 and brain-derived neurotrophic factor ( BDNF) Val66Met alleles have been associated with cognition. Associations of these alleles with cognition in heart failure (HF) and influences of HF across the cognitive spectrum (i.e., cognitively normal to Alzheimer's dementia [AD]) remain unexplored. Objectives To investigate influences of APOE ε2, ε4, BDNF Met and HF on cognition among participants across the cognitive spectrum. Methods Genetic association study using national databases ( N = 7,166). Results APOE ε2 frequencies were similar across the cognitive spectrum among participants with HF. APOE ε4 frequency was lower among participants with HF and AD than non-HF participants with AD. BDNF Met frequencies did not differ across the spectrum. HF was associated with worse attention and language. In the HF subsample, ε4 was associated with worse memory. Conclusion Associations between APOE and cognition may differ in HF but need to be tested in a larger sample

Oral curcumin for Alzheimer's disease: tolerability and efficacy in a 24-week randomized, double blind, placebo-controlled study

Introduction: Curcumin is a polyphenolic compound derived from the plant Curcuma Long Lin that has been demonstrated to have antioxidant and anti-inflammatory effects as well as effects on reducing beta-amyloid aggregation. It reduces pathology in transgenic models of Alzheimer's disease (AD) and is a promising candidate for treating human AD. The purpose of the current study is to generate tolerability and preliminary clinical and biomarker efficacy data on curcumin in persons with AD. Methods: We performed a 24-week randomized, double blind, placebo-controlled study of Curcumin C3 Complex® with an open-label extension to 48 weeks. Thirty-six persons with mild-to-moderate AD were randomized to receive placebo, 2 grams/day, or 4 grams/day of oral curcumin for 24 weeks. For weeks 24 through 48, subjects that were receiving curcumin continued with the same dose, while subjects previously receiving placebo were randomized in a 1:1 ratio to 2 grams/day or 4 grams/day. The primary outcome measures were incidence of adverse events, changes in clinical laboratory tests and the Alzheimer's Disease Assessment Scale - Cognitive Subscale (ADAS-Cog) at 24 weeks in those completing the study. Secondary outcome measures included the Neuropsychiatric Inventory (NPI), the Alzheimer's Disease Cooperative Study - Activities of Daily Living (ADCS-ADL) scale, levels of Aβ1-40 and Aβ1-42 in plasma and levels of Aβ1-42, t-tau, p-tau181 and F2-isoprostanes in cerebrospinal fluid. Plasma levels of curcumin and its metabolites up to four hours after drug administration were also measured. Results: Mean age of completers (n = 30) was 73.5 years and mean Mini-Mental Status Examination (MMSE) score was 22.5. One subject withdrew in the placebo (8%, worsened memory) and 5/24 subjects withdrew in the curcumin group (21%, 3 due to gastrointestinal symptoms). Curcumin C3 Complex® was associated with lowered hematocrit and increased glucose levels that were clinically insignificant. There were no differences between treatment groups in clinical or biomarker efficacy measures. The levels of native curcumin measured in plasma were low (7.32 ng/mL). Conclusions: Curcumin was generally well-tolerated although three subjects on curcumin withdrew due to gastrointestinal symptoms. We were unable to demonstrate clinical or biochemical evidence of efficacy of Curcumin C3 Complex® in AD in this 24-week placebo-controlled trial although preliminary data suggest limited bioavailability of this compound. Trial registration ClinicalTrials.gov Identifier: NCT00099710