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Journal articles on the topic 'Delta'

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Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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1

Haddon, C., L. Smithers, S. Schneider-Maunoury, T. Coche, D. Henrique, and J. Lewis. "Multiple delta genes and lateral inhibition in zebrafish primary neurogenesis." Development 125, no. 3 (February 1, 1998): 359–70. http://dx.doi.org/10.1242/dev.125.3.359.

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In Drosophila, cells are thought to be singled out for a neural fate through a competitive mechanism based on lateral inhibition mediated by Delta-Notch signalling. In tetrapod vertebrates, nascent neurons express the Delta1 gene and thereby deliver lateral inhibition to their neighbours, but it is not clear how these cells are singled out within the neurectoderm in the first place. We have found four Delta homologues in the zebrafish--twice as many as reported in any tetrapod vertebrate. Three of these--deltaA, deltaB and deltaD--are involved in primary neurogenesis, while two--deltaC and deltaD--appear to be involved in somite development. In the neural plate, deltaA and deltaD, unlike Delta1 in tetrapods, are expressed in large patches of contiguous cells, within which scattered individuals expressing deltaB become singled out as primary neurons. By gene misexpression experiments, we show: (1) that the singling-out of primary neurons, including the unique Mauthner cell on each side of the hindbrain, depends on Delta-Notch-mediated lateral inhibition, (2) that deltaA, deltaB and deltaD all have products that can deliver lateral inhibition and (3) that all three of these genes are themselves subject to negative regulation by lateral inhibition. These properties imply that competitive lateral inhibition, mediated by coordinated activities of deltaA, deltaB and deltaD, is sufficient to explain how primary neurons emerge from proneural clusters of neuroepithelial cells in the zebrafish.

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2

Haddon, C., Y. J. Jiang, L. Smithers, and J. Lewis. "Delta-Notch signalling and the patterning of sensory cell differentiation in the zebrafish ear: evidence from the mind bomb mutant." Development 125, no. 23 (December 1, 1998): 4637–44. http://dx.doi.org/10.1242/dev.125.23.4637.

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Mechanosensory hair cells in the sensory patches of the vertebrate ear are interspersed among supporting cells, forming a fine-grained pattern of alternating cell types. Analogies with Drosophila mechanosensory bristle development suggest that this pattern could be generated through lateral inhibition mediated by Notch signalling. In the zebrafish ear rudiment, homologues of Notch are widely expressed, while the Delta homologues deltaA, deltaB and deltaD, coding for Notch ligands, are expressed in small numbers of cells in regions where hair cells are soon to differentiate. This suggests that the delta-expressing cells are nascent hair cells, in agreement with findings for Delta1 in the chick. According to the lateral inhibition hypothesis, the nascent hair cells, by expressing Delta protein, would inhibit their neighbours from becoming hair cells, forcing them to be supporting cells instead. The zebrafish mind bomb mutant has abnormalities in the central nervous system, somites, and elsewhere, diagnostic of a failure of Delta-Notch signalling: in the CNS, it shows a neurogenic phenotype accompanied by misregulated delta gene expression. Similar misregulation of delta; genes is seen in the ear, along with misregulation of a Serrate homologue, serrateB, coding for an alternative Notch ligand. Most dramatically, the sensory patches in the mind bomb ear consist solely of hair cells, which are produced in great excess and prematurely; at 36 hours post fertilization, there are more than ten times as many as normal, while supporting cells are absent. A twofold increase is seen in the number of otic neurons also. The findings are strong evidence that lateral inhibition mediated by Delta-Notch signalling controls the pattern of sensory cell differentiation in the ear.

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Ernanto, Iwan. "SIFAT-SIFAT RING FAKTOR YANG DILENGKAPI DERIVASI." Journal of Fundamental Mathematics and Applications (JFMA) 1, no. 1 (June 30, 2018): 12. http://dx.doi.org/10.14710/jfma.v1i1.3.

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Let $R$ is a ring with unit element and $\delta$ is a derivation on $R$. An ideal $I$ of $R$ is called $\delta$-ideal if it satisfies $\delta (I)\subseteq I$. Related to the theory of ideal, we can define prime $\delta$-ideal and maximal $\delta$-ideal. The ring $R$ is called $\delta$-simple if $R$ is non-zero and the only $\delta$-ideal of $R$ are ${0}$ and $R$. In this paper, given the necessary and sufficient conditions for quotient ring $R/I$ is a $\delta$-simple where $\delta_*$ is a derivation on $R/I$ such that $\delta_* \circ \pi =\pi \circ \delta$.

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4

Latimer, Andrew J., Xinhong Dong, Youlia Markov, and Bruce Appel. "Delta-Notch signaling induces hypochord development in zebrafish." Development 129, no. 11 (June 1, 2002): 2555–63. http://dx.doi.org/10.1242/dev.129.11.2555.

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Different cell types that occupy the midline of vertebrate embryos originate within the Spemann-Mangold or gastrula organizer. One such cell type is hypochord, which lies ventral to notochord in anamniote embryos. We show that hypochord precursors arise from the lateral edges of the organizer in zebrafish. During gastrulation, hypochord precursors are closely associated with no tail-expressing midline precursors and paraxial mesoderm, which expresses deltaC and deltaD. Loss-of-function experiments revealed that deltaC and deltaD were required for her4 expression in presumptive hypochord precursors and for hypochord development. Conversely, ectopic, unregulated Notch activity blocked no tail expression and promoted her4 expression. We propose that Delta signaling from paraxial mesoderm diversifies midline cell fate by inducing a subset of neighboring midline precursors to develop as hypochord, rather than as notochord.

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5

Clark, Tiana. "Delta Delta Delta." Ploughshares 45, no. 1 (2019): 36–37. http://dx.doi.org/10.1353/plo.2019.0009.

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6

Beck, Rose, and Mallika Padival. "Differential Ability of the Notch Ligands Jagged2, Delta1, and Delta4 To Accelerate Development of Human CD34+ Hematopoietic Progenitor Cells (HPCs) into Killer Inhibitory Receptor (KIR)-Negative NK Cells with Cytotoxic Activity." Blood 110, no. 11 (November 16, 2007): 1326. http://dx.doi.org/10.1182/blood.v110.11.1326.1326.

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Abstract The evolutionarily conserved Notch receptors play important roles in cell fate decisions. Ligation of Notch-1 causes differentiation of T/NK cell precursors from HPCs and is critical for development of T cells in the thymic microenvironment. Five known Notch ligands exist in mammals (Delta1, Delta3, Delta4, Jagged1, and Jagged2), and Delta4 in particular has a greater capacity to support T cell development than Delta1. Notch ligation through Delta1 has also been shown to potentiate CD56+ NK cell differentiation from human HPCs in the presence of IL-15, although the phenotype and functionality of these cells has not been extensively described. We compared the ability of the 5 mammalian Notch ligands to induce the development of functional NK cells from human CD34+ HPCs derived from umbilical cord blood (CB). CD34+ cells isolated from CB were cultured in RPMI + 10% FBS on a murine stromal cell line, OP-9, expressing one of the five mammalian Notch receptors (Jagged1, Jagged2, Delta1, Delta3, or Delta4) or OP-9 cells transfected with vector alone, in the presence of IL-7, Flt3 ligand (FL), and IL-15. After three weeks of culture, development of CD56+CD3− cells was greatly accelerated by the ligands Jagged2 (53.4 +/− 5.5% CD56+CD3− cells), Delta-1 (38.6 +/− 5.7%), and Delta-4 (65.0 +/− 3.9%) versus culture in the absence of ligand (17.6 +/−10.3%, p = < 0.02) or in the presence of Jagged1 or Delta3. By 5 weeks, the percentage of NK cells seen in cultures containing Jagged2, Delta1, or Delta4 reached 80–90%. These NK cells expressed CD117 but only partially expressed CD94, with positivity ranging from 12.1 to 34.1% of NK cells derived from these 3 ligands after 5 weeks in culture; similarly, few CD16+ NK cells were seen in these cultures (0 to 12.1% of NK cells after 5 weeks). KIR expression in more than 1% of NK cells was not identified under any culture condition. In preliminary experiments, the addition of IL-2 or IL-21, both of which have been shown to induce KIR expression in non-Notch mediated models of NK cell development, did not significantly alter the percentages of NK cells expressing CD94, CD16, or KIR. Because the ligands Jagged2 and Delta4 induced the highest percentages of NK cells in culture, we examined the cytotoxic activity of these cells. NK cells derived from Jagged2 or Delta4 ligation expressed perforin and displayed in vitro cytotoxic activity against the human leukemia cell lines K562 (34.1% or 40.8% target cell lysis, respectively, at an E:T of 10:1) and HL-60 (14.1% or 31.6%, respectively). These cells also produced IFN-gamma, with Delta4 cultures producing higher levels of IFN-gamma versus Jagged2 cultures (1112 vs. 163.9 pg/ml, respectively). These data demonstrate that the Notch ligands vary in their ability to induce differentiation of NK cells from human CD34+ HPCs. Jagged2 and Delta4 in particular have greater capacity to generate functional NK cells which have cytolytic activity and can secrete IFN-gamma, while at the same time lacking a majority of inhibitory NK receptors (KIR and the NKG family of receptors which dimerize with CD94). The generation of cytolytic KIR-negative NK cells is of interest for cellular therapy against malignancies that are susceptible to NK cell killing.

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7

Максаков, Серафим Павлович, S. P. Maksakov, Марина Михайловна Сорокина, and Marina Mikhailovna Sorokina. "Об алгебраичности решеток $\omega$-веерных формаций конечных групп." Diskretnaya Matematika 34, no. 1 (2022): 23–35. http://dx.doi.org/10.4213/dm1659.

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Для непустого множества $\omega$ простых чисел В.А. Ведерниковым с помощью функциональных методов были построены $\omega$-веерные формации групп. В работе изучаются решеточные свойства $\omega$-веерных формаций конечных групп с направлением $\delta$, удовлетворяющим условию $\delta_{_{0}} \leq \delta$. Доказана алгебраичность решетки $\omega\delta F_{\theta}$ всех $\omega$-веерных формаций с направлением $\delta$ и $\theta$-значным $\omega$-спутником при условии, что решетка формаций $\theta$ является алгебраической. В качестве следствий установлена алгебраичность решеток $\omega\delta F$, $\omega\delta F_{\tau}$, $\tau\omega\delta F$, $\omega\delta^{n} F$ $\omega$-веерных формаций групп.

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8

Riley, B. B., M. Chiang, L. Farmer, and R. Heck. "The deltaA gene of zebrafish mediates lateral inhibition of hair cells in the inner ear and is regulated by pax2.1." Development 126, no. 24 (December 15, 1999): 5669–78. http://dx.doi.org/10.1242/dev.126.24.5669.

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Recent studies of inner ear development suggest that hair cells and support cells arise within a common equivalence group by cell-cell interactions mediated by Delta and Notch proteins. We have extended these studies by analyzing the effects of a mutant allele of the zebrafish deltaA gene, deltaA(dx2), which encodes a dominant-negative protein. deltaA(dx2/dx2)homozygous mutants develop with a 5- to 6-fold excess of hair cells and a severe deficiency of support cells. In addition, deltaA(dx2/dx2) mutants show an increased number of cells expressing pax2.1 in regions where hair cells are normally produced. Immunohistological analysis of wild-type and deltaA(dx2/dx2) mutant embryos confirmed that pax2.1 is expressed during the initial stages of hair cell differentiation and is later maintained at high levels in mature hair cells. In contrast, pax2.1 is not expressed in support cells. To address the function of pax2.1, we analyzed hair cell differentiation in no isthmus mutant embryos, which are deficient for pax2.1 function. no isthmus mutant embryos develop with approximately twice the normal number of hair cells. This neurogenic defect correlates with reduced levels of expression of deltaA and deltaD in the hair cells in no isthmus mutants. Analysis of deltaA(dx2/dx2); no isthmus double mutants showed that no isthmus suppresses the deltaA(dx2) phenotype, probably by reducing levels of the dominant-negative mutant protein. This interpretation was supported by analysis of T(msxB)(b220), a deletion that removes the deltaA locus. Reducing the dose of deltaA(dx2) by generating deltaA(dx2)/T(msxB)(b220)trans-heterozygotes weakens the neurogenic effects of deltaA(dx2), whereas T(msxB)(b220) enhances the neurogenic defects of no isthmus. mind bomb, another strong neurogenic mutation that may disrupt reception of Delta signals, causes a 10-fold increase in hair cell production and is epistatic to both no isthmus and deltaA(dx2). These data indicate that deltaA expressed by hair cells normally prevents adjacent cells from adopting the same cell fate, and that pax2.1 is required for normal levels of Delta-mediated lateral inhibition.

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9

Syvitski, J. P. M., and S. Daughney. "Delta2: Delta progradation and basin filling." Computers & Geosciences 18, no. 7 (August 1992): 839–97. http://dx.doi.org/10.1016/0098-3004(92)90028-p.

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10

Фуври, Этьен, and Maksym Radziwi l. "Новое применение дисперсионного метода Линника." Чебышевский сборник 19, no. 3 (January 9, 2019): 148–63. http://dx.doi.org/10.22405/2226-8383-2018-19-3-148-163.

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Пусть $\alpha_{m}$ и $\beta_{n}$ --- две последовательности вещественных чисел с носителями наотрезках $[M,2M]$ и $[N,2N]$, где $M = X^{1/2-\delta}$ и $N = X^{1/2+\delta}$. Мы доказываемсуществование такой постоянной $\delta_{0}$, что мультипликативная свертка$\alpha_{m}$ и $\beta_{n}$ имеет уровень распределения $1/2+\delta-\varepsilon$ (в слабом смысле),если только $0\leqslant \delta<\delta_{0}$, последовательность $\beta_{n}$ являетсяпоследовательностью Зигеля-Вальфиша, и обе последовательности $\alpha_{m}$ и $\beta_{n}$ограничены сверху функцией делителей.Наш результат, таким образом, представляет собой общую дисперсионную оценкудля "коротких"\, сумм II типа. Доказательство существенно использует дисперсионный метод Линникаи недавние оценки трилинейных сумм с дробями Клоостермана, принадлежащие Беттин и Чанди.Также мы остановимся на применении полученного результата к проблеме делителей Титчмарша.

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11

King, J. R. "Exact results for the nonlinear diffusion equations delta u/ delta t= delta / delta x(u-4/3delta u/ delta x) and delta u/ delta t- delta / delta x(u-2/3delta u/ delta x)." Journal of Physics A: Mathematical and General 24, no. 24 (December 21, 1991): 5721–45. http://dx.doi.org/10.1088/0305-4470/24/24/009.

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12

Мартыненко, Алексей Петрович, Alexey Petrovich Martynenko, Григорий Алексеевич Мартыненко, Gregory Alexeevich Martynenko, Вячеслав Вадимович Сорокин, Vyacheslav Vadimovich Sorokin, Рудольф Николаевич Фаустов, and Rudolf Nikolaevich Faustov. "Сверхтонкая структура $S$-состояний мюонного дейтерия." Вестник Самарского государственного технического университета. Серия «Физико-математические науки» 19, no. 3 (2015): 474–88. http://dx.doi.org/10.14498/vsgtu1381.

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В рамках квазипотенциального метода в квантовой электродинамике вычислены поправки порядка $\alpha^5$ и $\alpha^6$ в сверхтонкой структуре $S$-состояний мюонного дейтерия. Учтены релятивистские поправки, эффекты поляризации вакуума в первом, втором и третьем порядках теории возмущений, эффекты структуры и поправки на отдачу. Полученные численные значения сверхтонких расщеплений $\Delta E^{hfs}(1S)=50.2814$ мэВ ($1S$-состояние) и $\Delta E^{hfs}(2S)=6.2804$ meV ($2S$-состояние) можно использовать для сравнения с будущими экспериментальными данными коллаборации CREMA. Интервал сверхтонкой структуры $\Delta_{12}=8\Delta E^{hfs}(2S)- \Delta E^{hfs}(1S)=-0.0379$ meV можно использовать для прецизионной проверки квантовой электродинамики.

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13

Pawełczyk, T. "Isozymes delta of phosphoinositide-specific phospholipase C." Acta Biochimica Polonica 46, no. 1 (March 31, 1999): 91–98. http://dx.doi.org/10.18388/abp.1999_4186.

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Phospholipase C (PLC, EC 3.1.4.11) is the major starting point in the phosphatidylinositol pathway, which generates intracellular signals that regulate protein kinase C and intracellular calcium concentration. To date, three major types of phosphoinositide-specific PLC species named beta, gamma and delta, have been characterized. This article reviews recent studies on isozymes delta of PLC. Four such isozymes have been cloned and termed delta1-4. Their structural organization, regulation of activity and the interaction with membrane lipid are considered. The intracellular localization of delta isozymes and distribution in various tissues are presented. Attention is given to the pathological conditions in which an abnormal protein level of PLC delta or its activity have been observed.

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14

Galloway, W. E. "Fan-Delta, Braid Delta and the Classification of Delta Systems." Acta Geologica Sinica - English Edition 4, no. 4 (May 29, 2009): 387–400. http://dx.doi.org/10.1111/j.1755-6724.1991.mp4004004.x.

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15

Cornell, R. A., and J. S. Eisen. "Delta signaling mediates segregation of neural crest and spinal sensory neurons from zebrafish lateral neural plate." Development 127, no. 13 (July 1, 2000): 2873–82. http://dx.doi.org/10.1242/dev.127.13.2873.

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We examined the role of Delta signaling in specification of two derivatives in zebrafish neural plate: Rohon-Beard spinal sensory neurons and neural crest. deltaA-expressing Rohon-Beard neurons are intermingled with premigratory neural crest cells in the trunk lateral neural plate. Embryos homozygous for a point mutation in deltaA, or with experimentally reduced delta signalling, have supernumerary Rohon-Beard neurons, reduced trunk-level expression of neural crest markers and lack trunk neural crest derivatives. Fin mesenchyme, a putative trunk neural crest derivative, is present in deltaA mutants, suggesting it segregates from other neural crest derivatives as early as the neural plate stage. Cranial neural crest derivatives are also present in deltaA mutants, revealing a genetic difference in regulation of trunk and cranial neural crest development.

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16

Ochocka, Anna-Maria, and Tadeusz Pawelczyk. "Isozymes delta of phosphoinositide-specific phospholipase C and their role in signal transduction in the cell." Acta Biochimica Polonica 50, no. 4 (December 31, 2003): 1097–110. http://dx.doi.org/10.18388/abp.2003_3634.

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Phospholipase C (PLC, EC 3.1.4.11) is an enzyme crucial for the phosphoinositol pathway and whose activity is involved in eukaryotic signal transduction as it generates two second messengers: diacylglycerol (DAG) and inositol 1,4,5-trisphosphate (IP3). There are four major types of phospholipase C named: beta, gamma, delta and the recently discovered epsilon, but this review will focus only on the recent advances for the delta isozymes of PLC. So far, four delta isozymes (named delta1-4) have been discovered and examined. They differ with regard to cellular distribution, activities, biochemical features and involvement in human ailments.

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17

Karanasos, Konstantinos, Asterios Katsifodimos, and Ioana Manolescu. "Delta." Proceedings of the VLDB Endowment 7, no. 4 (December 2013): 217–28. http://dx.doi.org/10.14778/2732240.2732241.

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18

Parker, A. T. "Delta." Academic Psychiatry 34, no. 2 (March 1, 2010): 101. http://dx.doi.org/10.1176/appi.ap.34.2.101.

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19

Lazar, Alexandra. "Delta." Third Text 24, no. 4 (July 2010): 498–501. http://dx.doi.org/10.1080/09528822.2010.491387.

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20

Anderson, P. Q. R. "Delta." Hopkins Review 16, no. 1 (January 2023): 141–42. http://dx.doi.org/10.1353/thr.2023.0019.

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21

Ren, Jie, Saad Sarwana, Anubhav Sahu, Andrei Talalaevskii, and Amol Inamdar. "Low-Pass Delta-Delta-Sigma ADC." IEEE Transactions on Applied Superconductivity 25, no. 3 (June 2015): 1–6. http://dx.doi.org/10.1109/tasc.2014.2382552.

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22

YAMAMOTO, Toshio. "Educational lecture on .DELTA.(delta) bilirubin." Nihon Naika Gakkai Zasshi 78, no. 11 (1989): 1570–75. http://dx.doi.org/10.2169/naika.78.1570.

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23

Корпусов, Максим Олегович, Maxim Olegovich Korpusov, Роман Сергеевич Шафир, and Roman Sergeevich Shafir. "О разрушении решений задач Коши для нелинейных уравнений теории сегнетоэлектричества." Teoreticheskaya i Matematicheskaya Fizika 212, no. 3 (August 28, 2022): 327–39. http://dx.doi.org/10.4213/tmf10306.

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Изучаются две задачи Коши для нелинейных уравнений соболевского типа, первое из которых имеет вид $ \frac{\partial}{\partial t}\frac{\partial^2u}{\partial x_3^2} + \Delta u=|u|^q $, второе уравнение имеет вид $ \frac{\partial}{\partial t}\Delta_{\perp}u + \Delta u= |u|^q$. Найдены условия, при которых существуют слабые обобщенные локальные во времени решения задач Коши, а также найдены условия, при которых происходит разрушение решений.

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24

Skaskiv, O., and A. Kuryliak. "WIMAN’S TYPE INEQUALITY FOR SOME DOUBLE POWER SERIES." Bukovinian Mathematical Journal 9, no. 1 (2021): 56–63. http://dx.doi.org/10.31861/bmj2021.01.05.

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By $\mathcal{A}^2$ denote the class of analytic functions of the formBy $\mathcal{A}^2$ denote the class of analytic functions of the form$f(z)=\sum_{n+m=0}^{+\infty}a_{nm}z_1^nz_2^m,$with {the} domain of convergence $\mathbb{T}=\{z=(z_1,z_2)\in\mathbb C^2\colon|z_1|<1,\ |z_2|<+\infty\}=\mathbb{D}\times\mathbb{C}$ and$\frac{\partial}{\partial z_2}f(z_1,z_2)\not\equiv0$ in $\mathbb{T}.$ In this paper we prove some analogue of Wiman's inequalityfor analytic functions $f\in\mathcal{A}^2$. Let a function $h\colon \mathbb R^2_+\to \mathbb R_+$ be such that$h$ is nondecreasing with respect to each variables and $h(r)\geq 10$ for all $r\in T:=(0,1)\times (0,+\infty)$and $\iint_{\Delta_\varepsilon}\frac{h(r)dr_1dr_2}{(1-r_1)r_2}=+\infty$ for some $\varepsilon\in(0,1)$, where $\Delta_{\varepsilon}=\{(t_1, t_2)\in T\colon t_1>\varepsilon,\ t_2> \varepsilon\}$.We say that $E\subset T$ is a set of asymptotically finite $h$-measure on\ ${T}$if $\nu_{h}(E){:=}\iint\limits_{E\cap\Delta_{\varepsilon}}\frac{h(r)dr_1dr_2}{(1-r_1)r_2}<+\infty$ for some $\varepsilon>0$. For $r=(r_1,r_2)\in T$ and a function $f\in\mathcal{A}^2$ denote\begin{gather*}M_f(r)=\max \{|f(z)|\colon |z_1|\leq r_1,|z_2|\leq r_2\},\\mu_f(r)=\max\{|a_{nm}|r_1^{n} r_2^{m}\colon(n,m)\in{\mathbb{Z}}_+^2\}.\end{gather*}We prove the following theorem:{\sl Let $f\in\mathcal{A}^2$. For every $\delta>0$ there exists a set $E=E(\delta,f)$ of asymptotically finite $h$-measure on\ ${T}$ such that for all $r\in (T\cap\Delta_{\varepsilon})\backslash E$ we have \begin{equation*} M_f(r)\leq\frac{h^{3/2}(r)\mu_f(r)}{(1-r_1)^{1+\delta}}\ln^{1+\delta} \Bigl(\frac{h(r)\mu_f(r)}{1-r_1}\Bigl)\cdot\ln^{1/2+\delta}\frac{er_2}{\varepsilon}. \end{equation*}}

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25

Bousgheiri, Abdelhak, and Anass Ourraoui. "Multiplicity of solutions for a nonlinear nonlocal problem with variable exponent." Boletim da Sociedade Paranaense de Matemática 42 (April 29, 2024): 1–8. http://dx.doi.org/10.5269/bspm.62764.

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This work deals with a class of value problem involving the $p(x)$-biharmonic elliptic equation \begin{equation*} \begin{gathered} M_1(\int_{\Omega}\frac{1}{p(x)}|\Delta u|^{p(x)}dx)\Delta^2_{p(x)}u-M_2(\int_{\Omega}\frac{1}{p(x)}|\nabla u|^{p(x)}dx)\Delta_{p(x)}u=\lambda f(x,u)+\mu g(x,u) \quad\text{in }\Omega,\\ u=\Delta u=0,\quad x\in \partial \Omega, \end{gathered} \end{equation*} where $\Omega$ is a bounded domain in $\mathbb{R}^N,~N\geq1.$ with smooth boundary $\partial \Omega.$ Our technical method is based on a theorem obtained by B. Ricceri.

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26

Suonan, Labudan, and Yonglin Xu. "Existence of solutions to mixed local and nonlocal anisotropic quasilinear singular elliptic equations." AIMS Mathematics 8, no. 10 (2023): 24862–87. http://dx.doi.org/10.3934/math.20231268.

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<abstract><p>In this paper, we consider the existence of positive solutions to mixed local and nonlocal singular quasilinear singular elliptic equations</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \left\{\begin{array}{rl} -\Delta_{\vec{p}}u(x)+\left(-\Delta\right)_{p}^{s}u(x) = \frac{f(x)}{u(x)^{\delta}}, &x\in\Omega, \\ u(x)>0, \; \; \; \; \; \; &x\in\Omega, \\ u(x) = 0, \; \; \; \; \; \; &x\in\mathbb{R}^{N}\setminus\Omega, \end{array} \right. \end{align*} $\end{document} </tex-math></disp-formula></p> <p>where $ \Omega $ is a bounded smooth domain of $ \mathbb{R}^{N}(N > 2) $, $ -\Delta_{\vec{p}}u $ is an anisotropic $ p $-Laplace operator, $ \vec{p} = (p_{1}, p_{2}, ..., p_{N}) $ with $ 2\leq p_{1}\leq p_{2}\leq\cdot\cdot\cdot\leq p_{N} $, $ \left(-\Delta \right)_{p}^{s} $ is the fractional $ p $-Laplace operator. The major results shows the interplay between the summability of the datum $ f(x) $ and the power exponent $ \delta $ in singular nonlinearities.</p></abstract>

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27

Latif, Raja Mohammad. "Delta – Open Sets And Delta – Continuous Functions." International Journal of Pure Mathematics 8 (February 9, 2021): 1–22. http://dx.doi.org/10.46300/91019.2021.8.1.

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In 1968 Velicko [30] introduced the concepts of δ-closure and δ-interior operations. We introduce and study properties of δ-derived, δ-border, δ-frontier and δ-exterior of a set using the concept of δ-open sets. We also introduce some new classes of topological spaces in terms of the concept of δ-D- sets and investigate some of their fundamental properties. Moreover, we investigate and study some further properties of the well-known notions of δ-closure and δ-interior of a set in a topological space. We also introduce δ-R0 space and study its characteristics. We also introduce δ-R0 space and study its characteristics. We introduce δ-irresolute, δ-closed, pre-δ-open and pre -δ-closed mappings and investigate properties and characterizations of these new types of mappings and also explore further properties of the well-known notions of δ-continuous and δ-open mappings.

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28

Mastinsek, Miklavz. "Charm-Adjusted Delta and Delta Gamma Hedging." Journal of Derivatives 19, no. 3 (February 29, 2012): 69–76. http://dx.doi.org/10.3905/jod.2012.19.3.069.

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DÍAZ NAVARRO, PEDRO. "SOBRE DELTA-GRAFOS Y LA CONJETURA DELTA." Revista de Matemática: Teoría y Aplicaciones 25, no. 1 (February 1, 2018): 1. http://dx.doi.org/10.15517/rmta.v1i25.32228.

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In this paper we define two infinite families of graphs called C- graphs and -graphs and prove that -graphs satisfy delta conjecture. Also we see that C- graphs family contains the complements of -graphs. Finally we give a list of C- graphs and the relationship with the minimum semidefinite rank of these graphs.

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30

Pelletier, Philippe. "Hiroshima, ville-delta / Hiroshima, a delta city." Revue de géographie de Lyon 65, no. 4 (1990): 290–99. http://dx.doi.org/10.3406/geoca.1990.5747.

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31

Bouchet, André, and Werner Schwärzler. "The delta-sum of matching delta-matroids." Discrete Mathematics 181, no. 1-3 (February 1998): 53–63. http://dx.doi.org/10.1016/s0012-365x(97)00044-7.

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32

Samuel, A. Edward, and D. Balan. "\delta s-CONNECTEDNESS AND \delta s-COMPACTNESS." Universal Journal of Mathematics and Mathematical Sciences 8, no. 1-2 (April 14, 2016): 1–20. http://dx.doi.org/10.17654/um0080120001.

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33

Abdi, Ahmad, and Kanstantsin Pashkovich. "Delta Minors, Delta Free Clutters, and Entanglement." SIAM Journal on Discrete Mathematics 32, no. 3 (January 2018): 1750–74. http://dx.doi.org/10.1137/17m1126758.

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34

Bouhet, Elise. "Entretien avec Michel Simonot, auteur de Delta Charlie Delta1." Contemporary French and Francophone Studies 23, no. 3 (May 27, 2019): 273–80. http://dx.doi.org/10.1080/17409292.2019.1672324.

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35

Belay, N., R. Boopathy, and G. Voskuilen. "Anaerobic Transformation of Furfural by Methanococcus deltae (Delta)LH." Applied and environmental microbiology 63, no. 5 (1997): 2092–94. http://dx.doi.org/10.1128/aem.63.5.2092-2094.1997.

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36

Garibaldi, S., D. Tirabasso, S. Latrofa, V. Hartwig, M. Nesti, L. Panchetti, G. Mirizzi, et al. "REPOLARIZATION GRADIENT CAUSES LOCAL DEPOLARIZATION ABNORMALITIES IN BRUGADA SYNDROME." European Heart Journal Supplements 26, Supplement_2 (April 2024): ii6. http://dx.doi.org/10.1093/eurheartjsupp/suae036.012.

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Abstract Background Transmural voltage gradient in RVOT induces ECG–phenotype in Brugada syndrome(BrS). Moreover,RVOT depolarization abnormalities have been described as contributors to BrS phenotype and arrhythmogenesis. Purpose To investigate the effect of ajmaline administration on J–elevation of RVOT unipolar signals in BrS patients. Moreover,we wanted to assess whether ajmaline–induced unipolar J–point elevation variations induced local depolarization abnormalities. Methods 21 BrS patients with spontaneous type–1 ECG pattern were enrolled. Due to the absence of BrS ECG pattern at the study, patients underwent RV endocardial mapping with the CARTO3 system, before (PRE) and after (POST) ajmaline administration. The data were exported from CARTO and converted into Matlab format using OpenEP. J–elevation for each point was calculated as the amplitude of the unipolar signal at J wave with respect to baseline. Activation time (AT) of each point was defined as the difference between local depolarization (minimum dV/dt of the unipolar signal) and surface ECG depolarization(time of the minimum signal on V2). With an automatic algorithm, corresponding PRE and POST points were selected. The difference between POST and PRE of each parameter was calculated to obtain the differential values delta–J and delta–AT. Differential values were then interpolated on the mesh of each subject to obtain 3D maps. The deltaJ map was divided into four intervals based on quartiles. We then selected a ROI ‘IN‘ on a region with the greatest deltaJ variation, and a second ROI ‘OUT‘ on the zone of lowest variation. The same ROIs were applied to the deltaAT map. The mean value of the respective differential parameters was extracted in each ROI. Results Greatest delta–J values were found in the RVOT/anterior wall. delta–J in the ROI ‘IN‘ was greater than in the ROI ‘OUT‘ (1.68 [1.11–2.28] vs 0.56 [0.38–0.93] mV, p<0.001). delta–AT in the ROI ‘IN’ was greater than in the ROI ‘OUT’ (27.96 [20.39–44.89] vs 7.62 [4.24–16.69] ms, p<0.001). A good correlation was found between delta–J and delta–AT, considering the data for the two ROIs together (Spearman R coefficient=0.71, p<0.001). Conclusions: Our study shows that the repolarization gradient, evaluated by localized delta–J increase in RVOT, justifies BrS ECG phenotype and local depolarization abnormalities. A strong correlation was present in these RVOT areas between J–elevation variation and slow conducting zones.

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37

Shaw, A. "О мероморфных функциях с максимальной суммой дефектов и соответствующие разностные операторы." Владикавказский математический журнал, no. 1 (March 29, 2022): 121–35. http://dx.doi.org/10.46698/g4967-8526-0651-y.

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The paper deals with characteristic funtion and deficiency of a meromorphicfunction. We mainly focused on the relation between the characteristic function ofa product of difference operators with the characteristic function of a meromorphicfunction with maximal deficiency sum. The concept of maximal deficiency sum ofa meromorphic function is employed as an effective tool for our research. In the samecontext, the notion of a difference polynomial of a difference operator is discussed.The paper contains the details analysis and discussion of some asymptotic behaviourof the product of difference operators, such as$\lim_{r\rightarrow \infty }\frac{T(r,\prod_{i=1}^{q}\Delta _{\eta_{i}}f)}{T(r,f)}$,$\lim_{r\rightarrow \infty }\frac{N(r,0;\prod_{i=1}^{q}\Delta_{\eta_{i}}f)}{T(r,\prod_{i=1}^{q}\Delta _{\eta _{i}}f)}$,$\overline{\lim}_{r\rightarrow\infty}\frac{N(r,\infty;\prod_{i=1}^{q}\Delta_{\eta_{i}}f)+N(r,0;\prod_{i=1}^{q}\Delta_{\eta_{i}}f)}{T(r,\prod_{i=1}^{q}\Delta_{\eta_{i}}f)}$ etc.and same resolution and discussion also developed for the differencepolynomial of difference operators. Several innovative idea to establish some inequalitieson the zeros and poles for $\prod_{i=1}^{q}\Delta _{\eta _{i}}f$ and $L(\Delta_{\eta}f)$are also introduced. We broadly elaborate our results with many remarks and corollaries,and give two excellent examples for proper justification of our results. The results onproduct and polynomial of difference operators of our article improved andgeneralised the results of Z. Wu.

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38

Chung, Nguyen Thanh, and Zohreh Naghizadeh. "Multiplicity of solutions for a class of fourth-order elliptic equations of p(x)-Kirchhoff type." Mathematica Slovaca 71, no. 6 (December 1, 2021): 1441–58. http://dx.doi.org/10.1515/ms-2021-0063.

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Abstract This paper deals with a class of fourth order elliptic equations of Kirchhoff type with variable exponent Δ p ( x ) 2 u − M ( ∫ Ω 1 p ( x ) | ∇ u | p ( x ) d x ) Δ p ( x ) u + | u | p ( x ) − 2 u = λ f ( x , u ) + μ g ( x , u ) in Ω , u = Δ u = 0 on ∂ Ω , $$\begin{array}{} \left\{\begin{array}{} \Delta^2_{p(x)}u-M\bigg(\displaystyle\int\limits_\Omega\frac{1}{p(x)}|\nabla u|^{p(x)}\,\text{d} x \bigg)\Delta_{p(x)} u + |u|^{p(x)-2}u = \lambda f(x,u)+\mu g(x,u) \quad \text{ in }\Omega,\\ u=\Delta u = 0 \quad \text{ on } \partial\Omega, \end{array}\right. \end{array}$$ where p − := inf x ∈ Ω ¯ p ( x ) > max 1 , N 2 , λ > 0 $\begin{array}{} \displaystyle p^{-}:=\inf_{x \in \overline{\Omega}} p(x) \gt \max\left\{1, \frac{N}{2}\right\}, \lambda \gt 0 \end{array}$ and μ ≥ 0 are real numbers, Ω ⊂ ℝ N (N ≥ 1) is a smooth bounded domain, Δ p ( x ) 2 u = Δ ( | Δ u | p ( x ) − 2 Δ u ) $\begin{array}{} \displaystyle \Delta_{p(x)}^2u=\Delta (|\Delta u|^{p(x)-2} \Delta u) \end{array}$ is the operator of fourth order called the p(x)-biharmonic operator, Δ p(x) u = div(|∇u| p(x)–2∇u) is the p(x)-Laplacian, p : Ω → ℝ is a log-Hölder continuous function, M : [0, +∞) → ℝ is a continuous function and f, g : Ω × ℝ → ℝ are two L 1-Carathéodory functions satisfying some certain conditions. Using two kinds of three critical point theorems, we establish the existence of at least three weak solutions for the problem in an appropriate space of functions.

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39

Gunsar, Fulya. "Delta Hepatitis." Reviews in Health Care 3, no. 4 (October 12, 2012): 229. http://dx.doi.org/10.7175/rhc.26734229-241.

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Hepatitis delta virus (HDV) is a defective RNA virus that requires HBsAg for replication and transmission. It can cause acute or chronic hepatitis. Chronic infection with HDV is one of the most severe and difficult to treat forms of viral hepatitis. It has been estimated that there is a total of 15-20 million HDV carriers in the world. This review focuses on two fundamental aspects of HDV infection. On the one hand, epidemiological data are summarized, which are essential to understand the real burden of this disease. After the HBV vaccination programs in many countries all over the world, HDV infection has decreased since 1980’s but this decline has not continued further in the last decade. Therefore, HDV infection is still an important public health problem in the world. On the other hand, therapeutic options are described. Currently, interferons are the only option for the treatment of chronic hepatitis delta infection, and pegylated-interferons have shown better results than conventional interferons (IFNs). Monotherapy of nucleos(t)ide analogs have been found ineffective against the HDV infection, but adefovir and pegylated-IFN combination therapy have had some advantages for reduction of HBsAg levels. Trials with more potent nucleoside analogs and pegylated-IFN could be effective in the treatment of chronic HDV infection. New agents like prenylation inhibitors, that can affect the interactions between the large HDV antigen and HBsAg in the HDV virion, will be a hope in treatment of HDV infection.

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40

Gunsar, Fulya. "Delta Hepatitis." Reviews in Health Care 3, no. 4 (October 12, 2012): 229–41. http://dx.doi.org/10.7175/rhc.v3i4.267.

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Hepatitis delta virus (HDV) is a defective RNA virus that requires HBsAg for replication and transmission. It can cause acute or chronic hepatitis. Chronic infection with HDV is one of the most severe and difficult to treat forms of viral hepatitis. It has been estimated that there is a total of 15-20 million HDV carriers in the world. This review focuses on two fundamental aspects of HDV infection. On the one hand, epidemiological data are summarized, which are essential to understand the real burden of this disease. After the HBV vaccination programs in many countries all over the world, HDV infection has decreased since 1980’s but this decline has not continued further in the last decade. Therefore, HDV infection is still an important public health problem in the world. On the other hand, therapeutic options are described. Currently, interferons are the only option for the treatment of chronic hepatitis delta infection, and pegylated-interferons have shown better results than conventional interferons (IFNs). Monotherapy of nucleos(t)ide analogs have been found ineffective against the HDV infection, but adefovir and pegylated-IFN combination therapy have had some advantages for reduction of HBsAg levels. Trials with more potent nucleoside analogs and pegylated-IFN could be effective in the treatment of chronic HDV infection. New agents like prenylation inhibitors, that can affect the interactions between the large HDV antigen and HBsAg in the HDV virion, will be a hope in treatment of HDV infection.

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41

Shaikh, Hafeezullah, Ahsan Mobin, Imtiaz Manzoor, and Muhammad Ashraf Ebrahim. "HEPATITIS DELTA." Professional Medical Journal 25, no. 01 (January 8, 2018): 73–77. http://dx.doi.org/10.29309/tpmj/18.4208.

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Shaikh, Hafeezullah, Ahsan Mobin, Imtiaz Manzoor, and Muhammad Ashraf Ebrahim. "HEPATITIS DELTA." Professional Medical Journal 25, no. 01 (January 10, 2018): 73–77. http://dx.doi.org/10.29309/tpmj/2018.25.01.541.

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Objectives: The objective of this study is to prevalence of hepatitis delta inpatients with chronic hepatitis B infection. Study Design: Cross-sectional study. Period: Oneyear starting from February 2016 to January 2017. Setting: Patients OPD and admitted to Dowuniversity hospital and Zubaida Medical Center Karachi. Methods: Hepatitis B surface antigen(HbsAg) were analyzed for the presence or absence of Hepatitis D antibody (Anti HDV). 368patients with chronic hepatitis B were included to be part of this study. Patient’s age, duration ofillness and previous treatments were recorded. HBV and HDV virus presence was confirmed byusing Polymerase chain reaction (PCR). Results: Out of 368 patients with chronic HBV infection,291 (79.07%) were males and 77 (20.92%) were females. The male to female ratio was 3.7:1.Patients were aged between 35-60 years. 251 (68.2%) were positive for anti HDV. 211 of themwere males (84%) and 40 were females (15.9%). Conclusion: We have concluded that HDVinfection is associated with higher incidence of hepatocellular carcinoma in patients. Effectiveand early treatment of HDV can reduce the frequency of patients advancing to decompensatedchronic liver disease and hepatocellular carcinoma.

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43

Walsh, David W. "Delta Blues." Journal of General Internal Medicine 37, no. 1 (September 30, 2021): 244. http://dx.doi.org/10.1007/s11606-021-07154-0.

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44

Shamsian, Negin. "Delta dawn." Journal of Wound Care 30, no. 7 (July 2, 2021): 511. http://dx.doi.org/10.12968/jowc.2021.30.7.511.

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45

Johnson, C. E., W. J. Bourgeois, P. W. Wilson, J. E. Boudreaux, and F. J. Peterson. "`Delta' Peach." HortScience 29, no. 9 (September 1994): 1095. http://dx.doi.org/10.21273/hortsci.29.9.1095.

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46

Zito, Richard. "Delta Variant." Journal of System Safety 57, no. 3 (October 4, 2022): 7–34. http://dx.doi.org/10.56094/jss.v57i3.204.

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Nothing is harder than to realize when you are living through history. For most of us, each day is pretty much like another. There is nothing historically remarkable about that. Occasionally, however, our lives are punctuated by events, both natural and man-made, that are apocalyptic and often (but not always) beyond our control – natural disasters, war, pestilence, and famine. These are the events that the historian must recognize. At this time, it is the COVID-19 pandemic that demands to be recorded by “his-story” so that posterity will know what we did right, and what we did wrong. This author has taken up the challenge of producing accurate, unbiased, comprehensive, technical annals of the global coronavirus pandemic that began in 2019. “The Delta Variant” is the third publication in this series. We are now near the end of the third year of the pandemic (summer/fall 2021). As predicted by this author, it has been a draconian year. Last year’s peak in the number of active cases was not a global maximum for the pandemic in the U.S., since this year the number of active cases has already surpassed it. Without knowing where the global maximum lies, no accurate predictions can be made about the magnitude and duration of this modern plague. The “Delta Variant” (δ-variant) of COVID-19 has greatly complicated efforts to combat the virus. The “anti-vaxxer” movement, uncontrolled migration of people into and within the U.S, and the relaxation of safety measures during the late spring and early summer in the U.S. also contributed difficulties. All of these problems were foreseen by the author and were discussed in the second paper (“Vaccine Safety”) of this series on the COVID pandemic. However, our biggest problem in the U.S. was an over confidence born of a natural summertime trough in the daily infection rate. We wanted to believe the infection was past, so we ignored the experience of India, and our administrators fueled our hopes with their words and actions. We believed because we wanted to believe – except for this author. So, what went wrong? What is a δ-variant, and why is it so dangerous? That will be the topic of this publication.

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47

Clarke, Tom. "Delta blues." Nature 422, no. 6929 (March 2003): 254–56. http://dx.doi.org/10.1038/422254a.

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48

Nishioka, Norman S., and Jules L. Dienstag. "Delta Hepatitis." New England Journal of Medicine 312, no. 23 (June 6, 1985): 1515–16. http://dx.doi.org/10.1056/nejm198506063122311.

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49

Hoover, D. L. "Delta Prime?" Literary and Linguistic Computing 19, no. 4 (November 1, 2004): 477–95. http://dx.doi.org/10.1093/llc/19.4.477.

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50

Jablan, Slavik, Louis H. Kauffman, and Pedro Lopes. "Delta diagrams." Journal of Knot Theory and Its Ramifications 25, no. 09 (August 2016): 1641008. http://dx.doi.org/10.1142/s021821651641008x.

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We call a delta diagram any diagram of a knot or link whose regions (including the unbounded one) have 3, 4, or 5 sides. We prove that any knot or link admits a delta diagram. We define and estimate combinatorial link invariants stemming from this definition.

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