DIFFERENTIAL OPERATORS OF INFINITE ORDER IN THE SPACE OF RAPIDLY DECREASING SEQUENCES

We consider the space of rapidly decreasing sequences s and the derivative operator D defined on it. The object of this article is to study the equivalence of a differential operator of infinite order; that is φ（D） =^∞∑k=0φkD^k.φk constant numbers an a power of D.Dn, meaning, is there a isomorphism X （from s onto s） such that Xφ（D） = D^nX？. We prove that if φ（D） is equivalent to Dn, then φ（D） is of finite order, in fact a polynomial of degree n. The question of the equivalence of two differential operators of finite order in the space s is addressed too and solved completely when n = 1.

Isolation, Identification of Differentially Expressed Sequence Tags in the Backfat Tissue from Meishan, Large White and MeishanLarge White Cross Pigs

In order to detect the molecular mechanism of heterosis in pigs, the mRNA differential display technique was performedto investigate the differences of gene expression in the backfat tissue from Meishan, Large White and MeishanLargeWhite cross pigs. Nine 3'-end anchored primers in combination with ten 5'-end arbitrary primers were used to perform thedifferential display PCR and nearly 3 000 reproducible bands were examined. Fifteen expressed sequence tags that weredifferentially expressed were isolated and then identified through semi-quantitative RT-PCR. BLAST analysis revealedthat the fifteen expressed sequence tags (ESTs) were not homologous to any of the known porcine genes or ESTs. Thesenovel ESTs were then submitted to GenBank.

Differential expression and significance of 5-hydroxymethylcytosine modification in hepatitis B virus carriers and patients with liver cirrhosis and liver cancer

BACKGROUND The relationship between hepatitis B surface antigen(HBsAg)-positive carrier status and liver cancer has been extensively studied.However,the epigenetic changes that occur during progression from HBsAg-positive carrier status or cirrhosis to liver cancer are unknown.The epigenetic modification of DNA hydroxymethylation is critical in tumor development.Further,5-hydroxymethylcytosine(5hmC)is an important base for DNA demethylation and epigenetic regulation.It is also involved in the assembly of chromosomes and the regulation of gene expression.However,the mechanism of action of 5hmC in HBsAgpositive carriers or patients with cirrhosis who develop liver cancer has not been fully elucidated.AIM To investigate the possible epigenetic mechanism of HBsAg-positive carriers and hepatocellular carcinoma(HCC)progression from cirrhosis.METHODS Forty HBsAg-positive carriers,forty patients with liver cirrhosis,and forty patients with liver cancer admitted to the First People's Hospital of Yongkang between March 2020 and November 2021 were selected as participants.Free DNA was extracted using a cf-DNA kit.cfDNA was extracted by 5hmC DNA sequencing for principal component analysis,the expression profiles of the three groups of samples were detected,and the differentially expressed genes(DEGs)modified by hydroxymethylation were screened.Bioinformatic analysis was used to enrich DEGs,such as in biological pathways.RESULTS A total of 16455 hydroxymethylated genes were identified.Sequencing results showed that 32 genes had significant 5hmC modification differences between HBsAg carriers and liver cancer patients,of which 30 were upregulated and 2 downregulated in patients with HCC compared with HBsAg-positive carriers.Significant 5hmC modification differences between liver cirrhosis and liver cancer patients were identified in 20 genes,of which 17 were upregulated and 3 were downregulated in patients with HCC compared with those with cirrhosis.These genes may have potential loci that are undiscovered or unelucidated,which contribute to the development and progression of liver cancer.Analysis of gene ontology enrichment and Kyoto Encyclopedia of Genes and Genomes showed that the major signaling pathways involved in the differential genes were biliary secretion and insulin secretion.The analysis of protein interactions showed that the important genes in the protein-protein interaction network were phosphoenolpyruvate carboxykinase and solute carrier family 2.CONCLUSION The occurrence and development of liver cancer involves multiple genes and pathways,which may be potential targets for preventing hepatitis B carriers from developing liver cancer.

Differential mucin phenotypes and their significance in a variation of colorectal carcinoma

AIM: To investigate mucin expression profiles in colorectal carcinoma (CRC) histological subtypes with regard to clinicopathologic variables and prognosis. METHODS: Mucin (MUC)2 and MUC5AC expressions were assessed by immunohistochemistry for a total of 250 CRC cases that underwent surgical resection. CRCs included 63 well-to-moderately differentiated adenocar-cinomas (WMDAs), 91 poorly differentiated adenocarcinomas (PDAs), 81 mucinous adenocarcinoma (MUAs), and 15 signet-ring cell carcinomas (SRCCs). MUC2 and MUC5AC were scored as positive when ≥ 25% and ≥ 1% of cancer cells were stained positive, respectively. The human mutL homolog 1 and human mutS homolog 2 expressions were assessed by immunohistochemistry in PDAs to investigate mismatch-repair (MMR) status.Tumors that did not express either of these two were considered MMR-deficient. Results were analyzed for associations with clinicopathologic variables and the prognosis in individual histological CRC subtypes. RESULTS: MUC2-positive and MUC5AC-positive WMDA percentages were 49.2% and 30.2%, respectively. In contrast, MUC2-positive and MUC5AC-positive PDA percentages were 9.5% and 51.6%, respectively. MUC2 levels tended to decrease and MUC5AC levels tended to increase from WMDA to PDA. In 21 tumors comprising both adenoma and adenocarcinoma components in a single tumor (4 WMDAs, 7 PDAs, and 10 MUAs), MUC2 was significantly downregulated in PDA and MUC5AC was downregulated in PDA and MUA in the adenoma-carcinoma sequence. These results suggested that MUC2 levels might be associated with malignant potential and that MUC5AC expression was an early event in tumorigenesis. Despite worse prognoses than WMDA, high MUC2 expression levels were maintained in MUA (95.1%) and SRCC (71.5%), which suggested a pathogenesis for these subtypes distinct from that of WMDA. No significant associations were found between MUC2 expression and any clinicopathologic variables in any histological subtype. MUC5AC expression in PDA was closely associated with right-sided location (P = 0.017), absence of nodal metastasis (P = 0.010), low tumor node metastasis stage (P = 0.010), and MMR deficiency (P = 0.003). MUC2 expression in WMDA was a marginal prognostic factor for recurrence/metastasis-free survival (RFS) by univariate Cox analysis (P = 0.077) but not by multivariate Cox analysis (P = 0.161). MUC5AC expression in PDA was a significant prognostic factor for RFS by univariate Cox analysis (P = 0.007) but not by multivariate Cox analysis (P = 0.104). Kaplan-Meier curves and log-rank tests revealed that MUC2 expression was marginally associated with a better WMDA prognosis [P = 0.064 for RFS and P = 0.172 for overall survival (OS)] but not for PDA. In contrast, MUC5AC expression was significantly and marginally associated with a better PDA prognosis in terms of RFS and OS, respectively(P = 0.004 for RFS and P = 0.100 for OS), but not for WMDA and MUA. CONCLUSION: Mucin core protein expression profiles and clinical significance differ according to histological CRC subtypes. This may reflect different pathogeneses for these tumors.

Primarily screening and analyzing ESTs differentially expressed in rats' primary liver cancer

Objective： To screen and analyze key express sequence tags （ESTs） which were differentially displayed in every period of SD rats＇ primary hepatic carcinoma and reveal the molecular mechanism of carcinogenesis. Methods： Using diethylnitrosamine （DENA） as a cancerigenic agent, animal models with different phases of primary hepatic cancer were constructed in SD rats. Rats were respectively sacrificed at d 14, d 28, d 56, d 77, d 105 and d 112 after the rats received DENA by gavage, then the livers were harvested. One part of the livers was classified according to their pathological changes, while the other was reserved for molecular mechanism studies on hepatocarcinogenesis. The differentially expressed genes were isolated from both normal and morbid tissues by mRNA differential display technique （DDRT-PCR）. After the fragments were sequenced, bioinformatics were .used to analyze the results. Results： Twelve differentially expressed cDNA fragments were obtained. Nine fragments had the homology with known cDNA clones, especially EST-7 was similar to BN/SsNHsdMCW mitochondrion gene and the identity was 100% which suggested EST-7 may be the part of BN/SsNHsdMCW mitochondrion gene. In contrast, other three fragments （EST-1, EST-3 and EST-5） had extremely low identity to any genes registered in GENBANK databases. Conclusions： BN/SsNHsdMCW mitochondrion gene was expressed in different periods of hepatocarcinogenesis. Moreover, EST-I, EST-3 and EST-5 were suggested to contribute to the development of rat hepatocarcinogenesis, and thus may be candidates of new targets of oncogenes or cancer suppressor genes.

Differential temporal expression of matrix metalloproteinases following sciatic nerve crush

We previously performed transcriptome sequencing and found that genes for matrix metalloproteinases（MMPs）,such as MMP7 and 12,seem to be highly upregulated following peripheral nerve injury,and may be involved in nerve repair.In the present study,we systematically determined the expression levels of MMPs and their regulators at 1,4,7 and 14 days after sciatic nerve crush injury.The number of differentially expressed genes was elevated at 4 and 7 days after injury,but decreased at 14 days after injury.Among the differentially expressed genes,those most up-regulated showed fold changes of more than 214,while those most down-regulated exhibited fold changes of more than 2-10.Gene sequencing showed that,at all time points after injury,a variety of MMP genes in the “Inhibition of MMPs” pathway were up-regulated,and their inhibitor genes were down-regulated.Expression of key up-and down-regulated genes was verified by quantitative real-time polymerase chain reaction analysis and found to be consistent with transcriptome sequencing.These results suggest that MMP-related genes are strongly involved in the process of peripheral nerve regeneration.

Altered Expression of Differential Genes in Thoracic Spinal Cord Involved in Experimental Cholestatic Itch Mouse Model

The spinal origin of cholestatic itch in experimental obstructive jaundice mouse model remains poorly understood. In this study, the jaundice model was established by bile duct ligation （BDL） in mice, and differential gene expression patterns were analyzed in the lower thoracic spinal cord involved in cholestatic pruritus after BDL operation using high-throughput RNA sequencing. At 21st day after BDL, the expression levels of ENSRNOG00000060523, ENSRNOG00000058405 and ENSRNOG00000055193 mRNA were significantly up-regulated, and those of ENSRNOG00000042197, ENSRNOG00000008478, ENSRNOG00000019607, ENSRNOG00000020647, ENSRNOG00000046289, Gemin8, Serpina3n and Trim63 mRNA were significantly down-regulated in BDL group. The RNAseq data of selected mRNAs were validated by RT-qPCR. The expression levels of ENSRNOG00000042197, ENSRNOG00000008478, ENSRNOG00000019607, ENSRNOG00000020647, ENSRNOG00000046289 and Serpina3n mRNA were significantly down-regulated in BDL group. This study suggested that cholestatic pruritus in experimental obstructive jaundice mouse model is related with in the changes of gene expression profiles in spinal cord.

Differential expression of a novel colorectal cancer differentiation-related gene in colorectal cancer

AIM: To investigate SBA2 expression in CRC cell lines and surgical specimens of CRC and autologous healthy mucosa. METHODS: Reverse transcription-polymerase chain reaction (RT-PCR) was used for relative quantification of SBA2 mRNA levels in 4 human CRC cell lines with different grades of differentiation and 30 clinical samples. Normalization of the results was achieved by simultaneous amplification of beta-actin as an internal control. RESULTS: In the exponential range of amplification, fairly good linearity demonstrated identical amplification efficiency for SBA2 and beta-actin (82%). Markedly lower levels of SBA2 mRNA were detectable in tumors, as compared with the coupled normal counterparts P【0.01). SBA2 expression was significantly (0.01】P 【 0.05) correlated with the grade of differentiation in CRC, with relatively higher levels in well-differentiated samples and lower in poorly-differentiated cases. Of the 9 cases with lymph nodes affected, 78% (7/9) had reduced SBA2 mRNA expression in contrast to 24% (5/21) in non-metastasis samples 0.01】P【0.05). CONCLUSION: SBA2 gene might be a promising novel biomarker of cell differentiation in colorectal cancer and its biological features need further studies.

Improved Comb Filter based Approach for Effective Prediction of Protein Coding Regions in DNA Sequences

The prediction of protein coding regions in DNA sequences is an important problem in computational biology. It is observed that nucleotides in the protein coding regions or exons of a DNA sequence show period-3 property. Hence identification of the period-3 regions helps in predicting the gene locations within the billions long DNA sequence of eukaryotic cells. The period-3 property exhibited in exons of eukaryotic gene sequences enables signal processing based time-domain and frequency domain methods to predict these regions efficiently. Several approaches based on signal processing tools have, therefore, been applied to this problem, to predict these regions effectively. This paper describes novel and efficient comb filter-based techniques for the prediction of protein coding region based on the period-3 behavior of codon sequences. The proposed method is then validated on Burset/Guigo1996, HMR195 and KEGG standard datasets using various prediction measures. It is shown that cascaded differentiator comb (CDC) filter can be used for prediction of protein coding region with better prediction efficiency, and involves less computational complexity compared with the other signal processing techniques based on period-3 property.

ON OSCILLATION THEOREMS FOR HIGHER ORDER DIFFERENTIAL EQUATIONS

ＯＮＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＦＯＲＨＩＧＨＥＲＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＣｈｅｎＺｏｎｇｘｕａｎ（ＤｅｐｔｏｆＭａｔｈ，ＪｉａｎｇｘｉＮｏｒｍａｌＵｎｉｖ）ＮａｎｃｈａｎｇＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐ...

Analysis on differentially expressed genes in watermelon rind color based on RNA–Seq

In order to screen the genes controlling watermelon rind color and luster, the experiment was carried out with yellow watermelon skin mutants as tester and green wild type watermelon as control, and transcriptome sequencing and bioinformatics analysis were done. The results show that 34.27 Gb clean data were got by transcriptome sequencing. There are 261 differentially expressed genes among Y_1_vs_G_1, Y_2_vs_G_2 and Y_3_vs_G_3. The pathways contenting most differentially expressed genes are plant hormone signal transduction pathway, phenylpropanoid biosynthesis pathway, photosynthesis pathway, starch and sucrose metabolism pathway. 9-cis-epoxycarotenoid dioxygenase(Cla002942), alcohol dehydrogenase(Cla004992), photosystem Ⅰ reaction center subunit Ⅲ, chloroplastic(precursor)(Cla009181), long-chain acyl coenzyme A synthetase(Cla017341), threonine dehydratase biosynthetic(Cla018352) candidates genes were screened out.

UGD PROPERTY OF MUSIELAK-ORLICZ SEQUENCE SPACES

By the properties of the Musielak_Orlicz funciton's sequence, the necessary and sufficient condition for uniform Gateaux differential (UGD) property of Musielak_Orlicz sequence spaces equipped with the Luxemburg norm and a criterion for weakly uniform rotundity of Musielak_Orlicz sequence space with Orlicz norm are given.

Microarray-Based Differential Expression Monitoring of 79 Novel Genes in Human Fetal Tissues

ESTs fragments which represents corresponding novel genes were obtained by sequencing and bioinformatics analysis of human fet al kidney cDNA library. Microarray was prepared by using these novel EST fragmen ts by automatic spotting. Expression patters of 79 ESTs of novel genes from huma n fetal kidney were analyzed in fetal brain and fetal heart tissues of 20\|week\ | and 26\|week\|age fetus by performing of cDNA chip hybridization. This provide s clues for studying exact functions of the novel genes. 8 genes were obtained w hich were expressed differentially in the fetal brain and heart of 20\|week\| an d 26\|week\|age respectively. Then differentially expressed genes were identifie d by Northern analysis. The more exact function of the novel genes is under stud y.

Two Sums for a Class of Recurrence Sequences

A conjecture posed by Melham for Un2k+Un+12k in [2] is considered in this article.Several positive results on Vn+s2k +(-1)k(p2-4)kUn2k and V n2k+(-1)k(p2-4)kUn+s2k are achieved which generalize existed results on V n+12-(p2-4)Un2 and Vn2-(p2-4)Un+12.

Intraspecific Phylogenetic Relationships of Caryopteris incana in the Tsushima Islands, Japan, Using DNA Sequence Analysis

Caryopteris incana is a perennial shrub distributed in the temperate zone of the East Asia. It is found in West Kyushu in Japan, where it is designated as an endangered species. Tsushima, Nagasaki, which experienced repeated connection and fragmentation between the Korean Peninsula and Japan, is an island on the route along which C. incana moved to Japan from continental Asia. We conducted field work and confirmed the genetic structure of populations using DNA sequence analysis to construct a detailed distribution map and clarify the intraspecific phylogenetic relationships of C. incana in Tsushima Island. We confirmed 72 populations in Tsushima. Using the leaves of individuals cultivated from seeds collected from each natural population, we analyzed the chloroplast and nuclear DNA sequence variations. Among the populations, sequence variations were confirmed in six regions of chloroplast DNA, and six haplotypes, including base substitutions, were distinguished. Two haplotypes were mainly divided at the border of the northern part of the southern island in Tsushima. One population in the northwestern part of the north island showed a haplotype derived from the southern part. This finding revealed that the distribution of C. incana had been artificially influenced. Several haplotypes were confirmed by sequence variations in the northern populations, but only one haplotype in the southern populations, suggesting that C. incana on the north island had separated early from the south island in Tsushima.

Fault Identification of Power Grid Based on Wide-Area Differential Current and K-Means Clustering

A new method of fault domain identification is proposed based on K-means clustering analysis theories using the wide-area information of power grid. In the method, the node Intelligent Electronic Device (IED) associated domain is defined, and the relationship of positive sequence current fault component for the association domain boundaries is sought, then the conception of positive sequence fault component differential current for node IED association domains is introduced. The information of the positive sequence fault component differential current gathered by node IEDs is selected as the object of K-means clustering. The node IEDs of fault associated domains can be classified into one category, and the node IEDs of non-fault associated domains are classified into another category. With the fault area minimum principle, the group of node IEDs about fault associated domains can be obtained. The overlap of fault associated domains for different nodes is the fault area. A large number of simulations show that the algorithm proposed can identify fault domains with high accuracy and no influence by the operating mode of the system and topological changes.

Convergence Track Based Adaptive Differential Evolution Algorithm(CTbADE)

One of the challenging problems with evolutionary computing algorithms is to maintain the balance between exploration and exploitation capability in order to search global optima.A novel convergence track based adaptive differential evolution(CTbADE)algorithm is presented in this research paper.The crossover rate and mutation probability parameters in a differential evolution algorithm have a significant role in searching global optima.A more diverse population improves the global searching capability and helps to escape from the local optima problem.Tracking the convergence path over time helps enhance the searching speed of a differential evolution algorithm for varying problems.An adaptive powerful parameter-controlled sequences utilized learning period-based memory and following convergence track over time are introduced in this paper.The proposed algorithm will be helpful in maintaining the equilibrium between an algorithm’s exploration and exploitation capability.A comprehensive test suite of standard benchmark problems with different natures,i.e.,unimodal/multimodal and separable/non-separable,was used to test the convergence power of the proposed CTbADE algorithm.Experimental results show the significant performance of the CTbADE algorithm in terms of average fitness,solution quality,and convergence speed when compared with standard differential evolution algorithms and a few other commonly used state-of-the-art algorithms,such as jDE,CoDE,and EPSDE algorithms.This algorithm will prove to be a significant addition to the literature in order to solve real time problems and to optimize computationalmodels with a high number of parameters to adjust during the problem-solving process.

Minimum Resolution of the Minkowski, Schwarzschild and Kerr Differential Modules

Our recent arXiv preprints and published papers on the solution of the Riemann-Lanczos and Weyl-Lanczos problems have brought our attention on the importance of revisiting the algebraic structure of the Bianchi identities in Riemannian geometry. We also discovered in the meantime that, in our first GB book of 1978, we had already used a new way for studying the compatibility conditions (CC) of an operator that may not be necessarily formally integrable (FI) in order to construct canonical formally exact differential sequences on the jet level. The purpose of this paper is to prove that the combination of these two facts clearly shows the specific importance of the Spencer operator and the Spencer δ-cohomology, totally absent from mathematical physics today. The results obtained are unavoidable because they only depend on elementary combinatorics and diagram chasing. They also provide for the first time the purely intrinsic interpretation of the respective numbers of successive first, second, third and higher order generating CC. However, if they of course agree with the linearized Killing operator over the Minkowski metric, they largely disagree with recent publications on the respective numbers of generating CC for the linearized Killing operator over the Schwarzschild and Kerr metrics. Many similar examples are illustrating these new techniques, providing in particular a few resolutions in which the orders of the successive operators may go “up and down” surprisingly, like in the conformal situation for various dimensions.

SOLUTIONS FOR SECOND ORDER IMPULSIVE INTEGRO- DIFFERENTIAL EQUATION ON UNBOUNDED DOMAINS IN BANACH SPACES

Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis in Banach spaces. By the use of recurrence method, Tonelii sequence and the locally convex topology, the new existence theorems are achieved, which improve the related results obtained by Guo Da-jun.

柔性低频输电系统的主变稳态负序差动保护

为了解决常规纵差保护难以适用于低频系统的问题,通过分析低频系统的序分量抑制策略,并根据低频系统故障进入稳态后单侧有负序注入的特征,提出一种基于稳态负序分量的主变差动保护方法。为防止该差动保护在区外故障时因电流互感器饱和出现误动,通过对比分析三类制动电流计算方式的制动性能,得到了差动保护的制动方程和制动系数。为解决励磁涌流、电流互感器断线可能导致误动的问题,提出了相电压突变量的差动保护开放条件。仿真分析表明,该方法能够灵敏反映区内金属性故障及轻微故障,在区外故障伴随电流互感器饱和时有可靠的制动裕度。