Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation

Mathematics Subject Classification: 45G10, 45M99, 47H09

Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations

Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

Fractional Calculus of P-transforms

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99

Certain Differential Subordinations using a Generalized Sălăgean Operator and Ruscheweyh Operator

MSC 2010: 30C45, 30A20, 34A40

Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations

MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf Gorenflo

The relationship between selected standardized test scores and performance in advanced placement math and science exams: Analyzing the differential effectiveness of scores for course identification and placement

There is a national need to increase the STEM-related workforce. Among factors leading towards STEM careers include the number of advanced high school mathematics and science courses students complete. Florida's enrollment patterns in STEM-related Advanced Placement (AP) courses, however, reveal that only a small percentage of students enroll into these classes. Therefore, screening tools are needed to find more students for these courses, who are academically ready, yet have not been identified. The purpose of this study was to investigate the extent to which scores from a national standardized test, Preliminary Scholastic Assessment Test/ National Merit Qualifying Test (PSAT/NMSQT), in conjunction with and compared to a state-mandated standardized test, Florida Comprehensive Assessment Test (FCAT), are related to selected AP exam performance in Seminole County Public Schools. An ex post facto correlational study was conducted using 6,189 student records from the 2010 - 2012 academic years. Multiple regression analyses using simultaneous Full Model testing showed differential moderate to strong relationships between scores in eight of the nine AP courses (i.e., Biology, Environmental Science, Chemistry, Physics B, Physics C Electrical, Physics C Mechanical, Statistics, Calculus AB and BC) examined. For example, the significant unique contribution to overall variance in AP scores was a linear combination of PSAT Math (M), Critical Reading (CR) and FCAT Reading (R) for Biology and Environmental Science. Moderate relationships for Chemistry included a linear combination of PSAT M, W (Writing) and FCAT M; a combination of FCAT M and PSAT M was most significantly associated with Calculus AB performance. These findings have implications for both research and practice. FCAT scores, in conjunction with PSAT scores, can potentially be used for specific STEM-related AP courses, as part of a systematic approach towards AP course identification and placement. For courses with moderate to strong relationships, validation studies and development of expectancy tables, which estimate the probability of successful performance on these AP exams, are recommended. Also, findings established a need to examine other related research issues including, but not limited to, extensive longitudinal studies and analyses of other available or prospective standardized test scores.

Theoretical and experimental study on electron interactions with chlorobenzene: Shape resonances and differential cross sections

In this work, we report theoretical and experimental cross sections for elastic scattering of electrons by chlorobenzene (ClB). The theoretical integral and differential cross sections (DCSs) were obtained with the Schwinger multichannel method implemented with pseudopotentials (SMCPP) and the independent atom method with screening corrected additivity rule (IAM-SCAR). The calculations with the SMCPP method were done in the static-exchange (SE) approximation, for energies above 12 eV, and in the static-exchange plus polarization approximation, for energies up to 12 eV. The calculations with the IAM-SCAR method covered energies up to 500 eV. The experimental differential cross sections were obtained in the high resolution electron energy loss spectrometer VG-SEELS 400, in Lisbon, for electron energies from 8.0 eV to 50 eV and angular range from 7 degrees to 110 degrees. From the present theoretical integral cross section (ICS) we discuss the low-energy shape-resonances present in chlorobenzene and compare our computed resonance spectra with available electron transmission spectroscopy data present in the literature. Since there is no other work in the literature reporting differential cross sections for this molecule, we compare our theoretical and experimental DCSs with experimental data available for the parent molecule benzene. Published by AIP Publishing.

Local and nonlocal integro-differential reaction-diffusion models for protein dynamics in Alzheimer's disease

In this work, integro-differential reaction-diffusion models are presented for the description of the temporal and spatial evolution of the concentrations of Abeta and tau proteins involved in Alzheimer's disease. Initially, a local model is analysed: this is obtained by coupling with an interaction term two heterodimer models, modified by adding diffusion and Holling functional terms of the second type. We then move on to the presentation of three nonlocal models, which differ according to the type of the growth (exponential, logistic or Gompertzian) considered for healthy proteins. In these models integral terms are introduced to consider the interaction between proteins that are located at different spatial points possibly far apart. For each of the models introduced, the determination of equilibrium points with their stability and a study of the clearance inequalities are carried out. In addition, since the integrals introduced imply a spatial nonlocality in the models exhibited, some general features of nonlocal models are presented. Afterwards, with the aim of developing simulations, it is decided to transfer the nonlocal models to a brain graph called connectome. Therefore, after setting out the construction of such a graph, we move on to the description of Laplacian and convolution operations on a graph. Taking advantage of all these elements, we finally move on to the translation of the continuous models described above into discrete models on the connectome. To conclude, the results of some simulations concerning the discrete models just derived are presented.

Systemic Granulomatous Diseases Associated With Multiple Palpable Masses That May Involve The Breast: Case Presentation And An Approach To The Differential Diagnosis.

Palpable mass is a common complaint presented to the breast surgeon. It is very uncommon for patients to report breast mass associated with palpable masses in other superficial structures. When these masses are related to systemic granulomatous diseases, the diagnosis and initiation of specific therapy can be challenging. The purpose of this paper is to report a case initially assessed by the breast surgeon and ultimately diagnosed as granulomatous variant of T-cell lymphoma, and discuss the main systemic granulomatous diseases associated with palpable masses involving the breast.

Water Stress Reveals Differential Antioxidant Responses Of Tolerant And Non-tolerant Sugarcane Genotypes.

The biochemical responses of the enzymatic antioxidant system of a drought-tolerant cultivar (IACSP 94-2094) and a commercial cultivar in Brazil (IACSP 95-5000) grown under two levels of soil water restriction (70% and 30% Soil Available Water Content) were investigated. IACSP 94-2094 exhibited one additional active superoxide dismutase (Cu/Zn-SOD VI) isoenzyme in comparison to IACSP 95-5000, possibly contributing to the heightened response of IACSP 94-2094 to the induced stress. The total glutathione reductase (GR) activity increased substantially in IACSP 94-2094 under conditions of severe water stress; however, the appearance of a new GR isoenzyme and the disappearance of another isoenzyme were found not to be related to the stress response because the cultivars from both treatment groups (control and water restrictions) exhibited identical changes. Catalase (CAT) activity seems to have a more direct role in H2O2 detoxification under water stress condition and the shift in isoenzymes in the tolerant cultivar might have contributed to this response, which may be dependent upon the location where the excessive H2O2 is being produced under stress. The improved performance of IACSP 94-2094 under drought stress was associated with a more efficient antioxidant system response, particularly under conditions of mild stress.

Enhanced D1 And D2 Inhibitions Induced By Low-frequency Trains Of Conditioning Stimuli: Differential Effects On H- And T-reflexes And Possible Mechanisms.

Mechanically evoked reflexes have been postulated to be less sensitive to presynaptic inhibition (PSI) than the H-reflex. This has implications on investigations of spinal cord neurophysiology that are based on the T-reflex. Preceding studies have shown an enhanced effect of PSI on the H-reflex when a train of ~10 conditioning stimuli at 1 Hz was applied to the nerve of the antagonist muscle. The main questions to be addressed in the present study are if indeed T-reflexes are less sensitive to PSI and whether (and to what extent and by what possible mechanisms) the effect of low frequency conditioning, found previously for the H-reflex, can be reproduced on T-reflexes from the soleus muscle. We explored two different conditioning-to-test (C-T) intervals: 15 and 100 ms (corresponding to D1 and D2 inhibitions, respectively). Test stimuli consisted of either electrical pulses applied to the posterior tibial nerve to elicit H-reflexes or mechanical percussion to the Achilles tendon to elicit T-reflexes. The 1 Hz train of conditioning electrical stimuli delivered to the common peroneal nerve induced a stronger effect of PSI as compared to a single conditioning pulse, for both reflexes (T and H), regardless of C-T-intervals. Moreover, the conditioning train of pulses (with respect to a single conditioning pulse) was proportionally more effective for T-reflexes as compared to H-reflexes (irrespective of the C-T interval), which might be associated with the differential contingent of Ia afferents activated by mechanical and electrical test stimuli. A conceivable explanation for the enhanced PSI effect in response to a train of stimuli is the occurrence of homosynaptic depression at synapses on inhibitory interneurons interposed within the PSI pathway. The present results add to the discussion of the sensitivity of the stretch reflex pathway to PSI and its functional role.

EXISTENCE RESULTS FOR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper we discuss the existence of mild, strict and classical solutions for a class of abstract integro-differential equations in Banach spaces. Some applications to ordinary and partial integro-differential equations are considered.

Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

Differential regulation of PGC-1 alpha expression in rat liver and skeletal muscle in response to voluntary running

Background: The beneficial actions of exercise training on lipid, glucose and energy metabolism and insulin sensitivity appear to be in part mediated by PGC-1 alpha. Previous studies have shown that spontaneously exercised rats show at rest enhanced responsiveness to exogenous insulin, lower plasma insulin levels and increased skeletal muscle insulin sensitivity. This study was initiated to examine the functional interaction between exercise-induced modulation of skeletal muscle and liver PGC-1 alpha protein expression, whole body insulin sensitivity, and circulating FFA levels as a measure of whole body fatty acid (lipid) metabolism. Methods: Two groups of male Wistar rats (2 Mo of age, 188.82 +/- 2.77 g BW) were used in this study. One group consisted of control rats placed in standard laboratory cages. Exercising rats were housed individually in cages equipped with running wheels and allowed to run at their own pace for 5 weeks. At the end of exercise training, insulin sensitivity was evaluated by comparing steady-state plasma glucose (SSPG) concentrations at constant plasma insulin levels attained during the continuous infusion of glucose and insulin to each experimental group. Subsequently, soleus and plantaris muscle and liver samples were collected and quantified for PGC-1 alpha protein expression by Western blotting. Collected blood samples were analyzed for glucose, insulin and FFA concentrations. Results: Rats housed in the exercise wheel cages demonstrated almost linear increases in running activity with advancing time reaching to maximum value around 4 weeks. On an average, the rats ran a mean (Mean +/- SE) of 4.102 +/- 0.747 km/day and consumed significantly more food as compared to sedentary controls (P < 0.001) in order to meet their increased caloric requirement. Mean plasma insulin (P < 0.001) and FFA (P < 0.006) concentrations were lower in the exercise-trained rats as compared to sedentary controls. Mean steady state plasma insulin (SSPI) and glucose (SSPG) concentrations were not significantly different in sedentary control rats as compared to exercise-trained animals. Plantaris PGC-1 alpha protein expression increased significantly from a 1.11 +/- 0.12 in the sedentary rats to 1.74 +/- 0.09 in exercising rats (P < 0.001). However, exercise had no effect on PGC-1 alpha protein content in either soleus muscle or liver tissue. These results indicate that exercise training selectively up regulates the PGC-1 alpha protein expression in high-oxidative fast skeletal muscle type such as plantaris muscle. Conclusion: These data suggest that PGC-1 alpha most likely plays a restricted role in exercise-mediated improvements in insulin resistance (sensitivity) and lowering of circulating FFA levels.