Spectrum of Linear Difference Operators and the Solvability of Nonlinear Discrete Problems

Let T∈ℕ with T>5. Let 𝕋:={1,…,T}. We study the Fučik spectrum Σ of the discrete problem Δ2u(t-1)+λu+(t)-μu-(t)=0, t∈𝕋, u(0)=u(T+1)=0, where u+(t)=max⁡{u(t),0}, u-(t)=max⁡{-u(t),0}. We give an expression of Σ via the matching-extension method. We also use such discrete spectrum theory to study nonlinear boundary value problems of difference equations at resonance

Prickly Ash Seeds improve immunity of Hu sheep by changing the diversity and structure of gut microbiota

Prickly Ash Seeds (PAS), as a traditional Chinese medicinal herb, have pharmacological effects such as anti-asthma, anti-thrombotic, and anti-bacterial, but their impact on gut microbiota is still unclear. This study used a full-length 16 s rRNA gene sequencing technique to determine the effect of adding PAS to the diet on the structure and distribution of gut microbiota in Hu sheep. All lambs were randomly divided into two groups, the CK group was fed with a basal ration, and the LZS group was given a basal diet with 3% of PAS added to the ration. The levels of inflammatory factors (IL-10, IL-1β, and TNF-α) in intestinal tissues were measured by enzyme-linked immunosorbent assay (ELISA) for Hu sheep in the CK and LZS group. The results indicate that PAS can increase the diversity and richness of gut microbiota, and can affect the community composition of gut microbiota. LEfSe analysis revealed that Verrucomicrobiota, Kiritimatiella, WCHB 41, and uncultured_rumen_bacterium were significantly enriched in the LZS group. KEGG pathway analysis found that LZS was significantly higher than the CK group in the Excretory system, Folding, sorting and degradation, and Immune system pathways (p < 0.05). The results of ELISA assay showed that the level of IL-10 was significantly higher in the LZS group than in the CK group (p < 0.05), and the levels of TNF-α and IL-1β were significantly higher in the CK group than in the LZS group (p < 0.05). LEfSe analysis revealed that the dominant flora in the large intestine segment changed from Bacteroidota and Gammaproteobacteria to Akkermansiaceae and Verrucomicrobiae after PAS addition to Hu sheep lambs; the dominant flora in the small intestine segment changed from Lactobacillales and Aeriscardovia to Kiritimatiellae and WCHB1 41. In conclusion, the addition of PAS to sheep diets can increase the number and types of beneficial bacteria in the intestinal tract, improve lamb immunity, and reduce intestinal inflammation. It provides new insights into healthy sheep production

Dynamical Expression of MicroRNA-127-3p in Proliferating and Differentiating C2C12 Cells

MicroRNAs (miRNAs) are highly conserved, short non-coding RNAs that regulate gene expression at the posttranscriptional level. Although many miRNAs are identified in muscles and muscle cells, their individual roles are still not fully understood. In the present study, we investigated a muscle highly-expressed miRNA, miR-127-3p, in C2C12 myoblasts and tissues of goats with different muscle phenotypes (Boer vs Wushan black goats). Our results demonstrated that i) miR-127-3p was extensively expressed in tissues of goats; ii) miR-127-3p was higher expressed in muscle, spleen, heart, and skin in the muscular goats (Boer goats) than the control (Wushan black goats). Then we further characterized the dynamical expression of miR-127-3p, MyoD, MyoG, Myf5, Mef2c, and Myosin in the proliferating and differentiating C2C12 myoblasts at day of 0, 1, 3, 5, and 7 in culture mediums. Especially, we found that miR-127-3p was significantly higher expressed in the proliferating than differentiating cells. Our findings suggest that miR-127-3p probably plays roles in the proliferation and differentiation of myoblasts, which further underlies regulation of muscle phenotype in goats

Improved detectability of small-bowel lesions via capsule endoscopy with computed virtual chromoendoscopy: A pilot study

Objective. Real-time video capsule endoscopy (CE) with flexible spectral imaging color enhancement (FICE) improves visibility of small-bowel lesions. This article aims to clarify whether CE-FICE also improves detectability of small-bowel lesions. Patients and methods. A total of 55 patients who underwent CE at Hiroshima University Hospital during the period November 2009 through March 2010 were enrolled in the study. Five patients were excluded from the study because residues and transit delays prevented sufficient evaluation. Thus, 50 patients participated. Two experienced endoscopists (each having interpreted more than 50 capsule videos) analyzed the images. One interpreted conventional capsule videos; the other, blinded to interpretation of the conventional images, interpreted CE-FICE images obtained at settings 1-3 (setting 1: red 595 nm, green 540 nm, blue 535 nm; setting 2: red 420 nm, green 520 nm, blue 530 nm; setting 3: red 595 nm, green 570 nm, blue 415 nm). Lesions were classified as angioectasia, erosion, ulceration, or tumor. Detectability was compared between the two modalities. Time taken to interpret the capsule videos was also determined. Results. Seventeen angioectasias were identified by conventional CE; 48 were detected by CE-FICE at setting 1, 45 at setting 2, and 24 at setting 3, with significant differences at settings 1 and 2 (p = 0.0003, p < 0.0001, respectively). Detection of erosion, ulceration, and tumor did not differ statistically between conventional CE and CE-FICE, nor did interpretation time (conventional CE 36 ± 6.9 min; CE-FICE setting 1, 36 ± 6.4 min; setting 2, 38 ± 5.8 min; setting 3, 35 ± 6.7 min). Conclusions. CE-FICE is superior in the lesion detection in comparison with conventional CE and improves detection of angioectasia

Sensor placement optimization for thermal error compensation on machine tools.

One of the most significant factors affecting the accuracy of machine tools is thermal error. Thermal error compensation can potentially be an effective way to reduce thermal errors. However, lack of accuracy and robustness of thermal error modeling prevents thermal error compensation from achieving greater success. This thesis proposes a novel methodology for improving the accuracy of thermal error modeling through optimizing temperature sensor placement. It addresses the question: Given a limited number of temperature sensors, where should they be placed on a spatially distributed machine tool structure so that the temperature data from those sensors will give the best estimation of the thermal errors? A thermal deformation modal analysis method is proposed to analyze the transient temperature fields and thermal deformations of a machine tool structure. Natural time constants and temperature field mode shapes can be computed from transient heat transfer finite element models through eigen-analysis. Thermal deformation and thermal error mode shapes can be computed from thermoelastic finite element models. A modal frequency domain method of inverse heat transfer analysis is also proposed. From temperature measurement data from multiple sensors mounted on a machine tool structure, transient thermal loads of multiple heat sources can be estimated simultaneously. With mode truncation and frequency truncation, both efficiency and stability of the method can be improved. The temperature sensor placement optimization problem is formulated as a two-level optimization model. The first level is a sensor location optimization problem and is formulated as a discrete programming model. The second level is a thermal error model parameter optimization problem and is formulated as a nonlinear programming model. The minimax goal programming approach is applied to formulate the objective function. A hybrid genetic algorithm combining the advantages of both the cyclic local search algorithm and the genetic algorithm is developed. The methodology is applied to a machining center column assembly. Experimental results prove that the optimized sensor location set improves the accuracy and robustness of thermal error modeling.Ph.D.Applied SciencesMechanical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/123525/2/3001002.pd

Spectrum of Linear Difference Operators and the Solvability of Nonlinear Discrete Problems

Let T ∈ N with T &gt; 5. Let T : {1, . . . , T}. We study the Fučik spectrum Σ of the discrete problem We give an expression of Σ via the matching-extension method. We also use such discrete spectrum theory to study nonlinear boundary value problems of difference equations at resonance

A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems

<p/> <p>Let <inline-formula><graphic file="1687-1847-2009-671625-i1.gif"/></inline-formula> be an integer with <inline-formula><graphic file="1687-1847-2009-671625-i2.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-671625-i3.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-671625-i4.gif"/></inline-formula>. We consider boundary value problems of nonlinear second-order difference equations of the form <inline-formula><graphic file="1687-1847-2009-671625-i5.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-671625-i6.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-671625-i7.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1847-2009-671625-i8.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-671625-i9.gif"/></inline-formula> and, <inline-formula><graphic file="1687-1847-2009-671625-i10.gif"/></inline-formula> for <inline-formula><graphic file="1687-1847-2009-671625-i11.gif"/></inline-formula>, and <inline-formula><graphic file="1687-1847-2009-671625-i12.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-671625-i13.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-671625-i14.gif"/></inline-formula>. We investigate the global structure of positive solutions by using the Rabinowitz's global bifurcation theorem.</p

Histomorphological Comparisons and Expression Patterns of <i>BOLL</i> Gene in Sheep Testes at Different Development Stages

BOLL is implicated in mammalian testicular function maintenance and spermatogenesis. To understand the expression patterns and biological functions of sheep BOLL, we examined the expression and immunolocalization of BOLL in the developing testes of Small-Tail Han sheep aged 0 days (D0), 2 months (2M), 5 months (5M), 1 year (1Y), and 2 years (2Y), by qPCR, Western blot, and immunohistochemistry methods. Firstly, morphological studies revealed that, in addition to spermatogonia, ordered and clear spermatocytes, as well as round and elongated spermatids and sperm, were found in the 1Y and 2Y testicular seminiferous tubules of the sheep testes, compared with the D0, 2M, and 5M testes, as analyzed by hematoxylin and eosin (H&amp;E) staining. The diameter and area of the seminiferous tubules, epithelial thickness, and the area and perimeter of the tubule lumens gradually increased with age. BOLL was specifically expressed in testes and upregulation of BOLL transcript expression was higher in the testes of the 1Y and 2Y groups than in those of the D0, 2M, and 5M groups. Similarly, BOLL protein was expressed mainly in the 1Y and 2Y testes, ranging from primary spermatocytes to round spermatids, as well as in the spermatozoa. This study is the first demonstration that sheep BOLL might serve as a key regulator of the spermiogenesis involved in sperm maturity, in addition to its role as a crucial meiotic regulator

Characterization of GLOD4 in Leydig Cells of Tibetan Sheep during Different Stages of Maturity

We have previously reported that glyoxalase domain-containing protein 4 (GLOD4) is expressed in sheep testes by proteome analysis, but its roles during testicular development remain unclear. The aim of this study was to understand the expression characteristics and biological functions of the GLOD4 gene in developmental Tibetan sheep testes. The cDNA sequence of the Tibetan sheep GLOD4 gene was cloned by the RT-PCR method, and the structural characteristics of the GLOD4 protein were analyzed using relevant bioinformatics software, including ProtParam, TMHMM, Signal P 4.1, SOPMA, and phyre2. The expression patterns and immunolocalization of GLOD4 were examined in developmental testes derived from three-month-old (3M), one-year-old (1Y), and three-year-old (3Y) Tibetan sheep using quantitative real-time PCR (qRT-PCR), Western blot, immunohistochemistry, and immunofluorescence staining. The sequence analysis showed that the coding sequence (CDS) region of the GLOD4 gene was 729 bp in length and encoded 242 amino acids. Bioinformatics analysis found that the nucleotide and amino acid sequence of Tibetan sheep GLOD4 exhibited the highest sequence similarity with goat and chiru, and the least with zig-zag eel, of the species compared. GLOD4 expressions at both the mRNA and protein levels were significantly higher in the testes of the 1Y and 3Y groups than those in the 3M group (p &lt; 0.01). Immunohistochemistry and immunofluorescence results indicated that the GLOD4 protein was mainly localized in the cytoplasm of Leydig cells from Tibetan sheep testes throughout the development stages. These results taken together suggest that the GLOD4 gene may be implicated in the development of the Leydig cells of Tibetan sheep during different stages of maturity

Proteomic Analyses of Mammary Glands Provide Insight into the Immunity and Metabolism Pathways Associated with Clinical Mastitis in Meat Sheep

Clinical mastitis is still an intractable problem for sheep breeding. The natural immunologic mechanisms of the mammary gland against infections are not yet understood. For a better understanding of the disease-associated proteins during clinical mastitis in meat sheep, we performed two-dimensional electrophoresis (2-DE)-based comparative proteomic analyses of mammary tissues, including from healthy mammary tissues (HMTs) and from mammary tissues with clinical mastitis (CMMTs). The 2-DE results showed that a total of 10 up-regulated and 16 down-regulated proteins were identified in CMMTs when compared to HMTs. Of these, Gene Ontology (GO) and Kyoto Encyclopaedia of Genes and Genomes (KEGG) enrichment analyses revealed that most proteins were associated with immune responses or metabolisms. The results of qRT-PCR and Western blot for randomly selected four differentially expressed proteins (DEPs) including superoxide dismutase [Mn] (SOD2), annexin A2 (ANAX2), keratin 10 (KRT10) and endoplasmic reticulum resident protein 29 (ERP29) showed that their expression trends were consistent with 2-DE results except ANXA2 mRNA levels. This is an initial report describing the 2-DE-based proteomics study of the meat sheep mammary gland with clinical mastitis caused by natural infection, which provides additional insight into the immune and metabolic mechanisms during sheep mastitis