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Published: 22 June 2024

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1

ANTOLÍN, YAGO, WARREN DICKS, and PETER A. LINNELL. "ON THE LOCAL-INDICABILITY COHEN–LYNDON THEOREM." Glasgow Mathematical Journal 53, no. 3 (August 1, 2011): 637–56. http://dx.doi.org/10.1017/s0017089511000231.

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AbstractFor a group H and a subset X of H, we let HX denote the set {hxh−1 | h ∈ H, x ∈ X}, and when X is a free-generating set of H, we say that the set HX is a Whitehead subset of H. For a group F and an element r of F, we say that r is Cohen–Lyndon aspherical in F if F{r} is a Whitehead subset of the subgroup of F that is generated by F{r}. In 1963, Cohen and Lyndon (D. E. Cohen and R. C. Lyndon, Free bases for normal subgroups of free groups, Trans. Amer. Math. Soc. 108 (1963), 526–537) independently showed that in each free group each non-trivial element is Cohen–Lyndon aspherical. Their proof used the celebrated induction method devised by Magnus in 1930 to study one-relator groups. In 1987, Edjvet and Howie (M. Edjvet and J. Howie, A Cohen–Lyndon theorem for free products of locally indicable groups, J. Pure Appl. Algebra45 (1987), 41–44) showed that if A and B are locally indicable groups, then each cyclically reduced element of A*B that does not lie in A ∪ B is Cohen–Lyndon aspherical in A*B. Their proof used the original Cohen–Lyndon theorem. Using Bass–Serre theory, the original Cohen–Lyndon theorem and the Edjvet–Howie theorem, one can deduce the local-indicability Cohen–Lyndon theorem: if F is a locally indicable group and T is an F-tree with trivial edge stabilisers, then each element of F that fixes no vertex of T is Cohen–Lyndon aspherical in F. Conversely, by Bass–Serre theory, the original Cohen–Lyndon theorem and the Edjvet–Howie theorem are immediate consequences of the local-indicability Cohen–Lyndon theorem. In this paper we give a detailed review of a Bass–Serre theoretical form of Howie induction and arrange the arguments of Edjvet and Howie into a Howie-inductive proof of the local-indicability Cohen–Lyndon theorem that uses neither Magnus induction nor the original Cohen–Lyndon theorem. We conclude with a review of some standard applications of Cohen–Lyndon asphericity.

2

Davenport, Derek A. "America's Scientific Treasures: A Travel Companion (Cohen, Paul S.; Cohen, Brenda H.)." Journal of Chemical Education 76, no. 7 (July 1999): 903. http://dx.doi.org/10.1021/ed076p903.1.

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3

Theriault, Stephen D. "Homotopy Decompositions Involving the Loops of Coassociative Co-H Spaces." Canadian Journal of Mathematics 55, no. 1 (February 1, 2003): 181–203. http://dx.doi.org/10.4153/cjm-2003-008-5.

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AbstractJames gave an integral homotopy decomposition of ∑Ω∑X, Hilton-Milnor one for Ω(∑X ∨ ∑Y), and Cohen-Wu gave p-local decompositions of Ω∑X if X is a suspension. All are natural. Using idempotents and telescopes we show that the James andHilton-Milnor decompositions have analogues when the suspensions are replaced by coassociative co-H spaces, and the Cohen-Wu decomposition has an analogue when the (double) suspension is replaced by a coassociative, cocommutative co-H space.

4

Knysak, Benjamin. "H. Robert Cohen: A Portrait in Five Titles." Fontes Artis Musicae 64, no. 1 (2017): 109–10. http://dx.doi.org/10.1353/fam.2017.0011.

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5

H. Beaty, T. "Bernice H. Cohen, a Pioneer in Genetic Epidemiology." American Journal of Epidemiology 174, no. 1 (June 9, 2011): 1. http://dx.doi.org/10.1093/aje/kwr158.

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6

Jessie, Evangelista E., Mary M. Ruisi, Daniel Green, Rachel Burt, Jaclyn Davis, Regina A. Macatangay, Farid Boulad, et al. "Radioulnar Synostosis-Hematology (RUS-H) Syndrome: Description of the New Syndrome and Comparison to Similar Syndromes." Blood 120, no. 21 (November 16, 2012): 1100. http://dx.doi.org/10.1182/blood.v120.21.1100.1100.

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Abstract Abstract 1100 Congenital radioulnar synostostis (RUS) is a rare anomaly characterized by fusion of the radius and ulna. RUS occurs more frequently in males than females, and is bilateral in 50% of cases. Since 1793, there have been > 400 cases reported. Literature review revealed 7 rare syndromes with RUS and hematologic problems including our newly named RUS-H Syndrome: 1) Diamond-Blackfan Anemia (DBA) associated with normochromic, macrocytic anemia in early infancy and erythroblastopenia; 2) Amegakaryocytic Thrombocytopenia Radioulnar Syndrome (ATRUS, HoxA11 mutation) with thrombocytopenia since birth requiring stem-cell transplantation; 3) IVIC Syndrome with mild thrombocytopenia and leukocytosis; 4) WT Syndrome involving a wide array of hematologic abnormalities including easy bruising, hypoplastic anemia, pancytopenia, Acute Lymphoblastic Leukemia (ALL), and Acute Myeloblastic Leukemia (AML); 5) Cohen Syndrome with neutropenia and fluctuating thrombocytopenia; 6) Noonan Syndrome with abnormal bleeding and easy bruising; and 7) RUS-H Syndrome (not involving HoxA11 mutations) associated with a spectrum of hematologic abnormalities including easy bruising, recurrent epistaxis, neutropenia, thrombocytopenia, ALL and aplastic anemia. This is a subsequent report to our ASH 2010 abstract. All 7 syndromes are associated with hand abnormalities. Six of the 7 syndromes (not Cohen) are associated with hearing loss/ear abnormalities. Four syndromes (DBA, ATRUS, WT, and RUS-H) have an increased risk of hematological malignancy. DBA, IVIC, Cohen, and Noonan have abnormalities of the eye and genitourinary system. DBA, WT, Cohen, and Noonan Syndromes are associated with dysmorphic facial features. ATRUS, IVIC, Cohen, and Noonan Syndromes all exhibit lower limb abnormalities. DBA, Cohen, Noonan, and RUS-H are associated with short stature. DBA, IVIC, Noonan, and RUS-H Syndromes are associated with kidney abnormalities and structural heart defects. Three Syndromes (DBA, IVIC, and Cohen) have cranial abnormalities. DBA IVIC, and Noonan Syndrome have structural defects of the shoulder. IVIC, Cohen, and Noonan Syndromes are associated with spinal anomalies. Two Syndromes (DBA and Noonan Syndrome) are associated with liver, spleen, and neck abnormalities. Cohen and Noonan Syndrome are associated with developmental delays. Lastly, WT and Noonan Syndrome are associated with skin abnormalities (Figure 1). This abstract highlights the association of RUS, other congenital abnormalities, and hematologic problems in previously described syndromes and in the novel RUS-H Syndrome. DBA, Cohen, and Noonan Syndrome are the most common of the 7 syndromes, with DBA estimated at 5 per 1,000,000; Cohen Syndrome predicted to have a prevalence of <1,000; and Noonan Syndrome predicted to have a prevalence of <1 in 2,500; however, RUS in DBA, Cohen, and Noonan Syndrome is limited to case reports. RUS-H Syndrome has been identified in 12 families in the United States, Canada, and England. IVIC and WT Syndromes have been reported in 4 families total, and ATRUS with an identified HoxA11 mutation has been reported in at least 2 families. Since RUS may often be missed on routine physical examination, we recommend specific evaluation of pronation/supination in patients with hematological problems of unknown etiology. Additionally, we recommend that a targeted genetic panel be developed to detect mutations that are known for syndromes involving RUS, blood abnormalities, and other similar orthopedic entities that have cross-over manifestations like Thrombocytopenia-Absent Radii (TAR) Syndrome. This panel might consist of mutations associated with DBA (RPL5, RPL11, RPL35A, RPS7, RPS10, RPS17, RPS19, RPS24, and RPS26 mutations), with ATRUS (HoxA11 mutation), with IVIC Syndrome (SALL4 mutations), with Cohen Syndrome (8q22.2q22.3/COH1 deletion), with Noonan Syndrome (PTPN11, SOS1, RAF1, KRAS, NRAS, and BRAF mutations) and with TAR Syndrome (RBM8A null allele and noncoding SNP). The causative mutations of WT and RUS-H Syndromes have yet to be discovered. Genetic analysis of 6 of the 12 families with RUS-H Syndrome did not reveal a HoxA11 mutation. Broader sequencing techniques are underway for all 12 families in our RUS-H cohort, with hopeful detection of a new candidate gene as the unifying causative factor for the abnormalities in limb formation and hematopoiesis. Disclosures: Bussel: Ligand: Membership on an entity's Board of Directors or advisory committees, Research Funding; Immunomedics: Research Funding; IgG of America: Research Funding; Genzyme: Research Funding; GlaxoSmithKline: Family owns GSK stock, Family owns GSK stock Other, Membership on an entity's Board of Directors or advisory committees, Research Funding; Cangene: Research Funding; Amgen: Family owns Amgen stock Other, Membership on an entity's Board of Directors or advisory committees, Research Funding; Eisai: Membership on an entity's Board of Directors or advisory committees, Research Funding; Shionogi: Membership on an entity's Board of Directors or advisory committees, Research Funding; Sysmex: Research Funding; Portola: Consultancy.

7

de Quehen, Victoria E., and Leslie G. Roberts. "Non-Cohen–Macaulay Projective Monomial Curves with Positive h-Vector." Canadian Mathematical Bulletin 48, no. 2 (June 1, 2005): 203–10. http://dx.doi.org/10.4153/cmb-2005-018-1.

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8

Constantinescu, Alexandru, and Matteo Varbaro. "On the $h$-vectors of Cohen-Macaulay Flag Complexes." MATHEMATICA SCANDINAVICA 112, no. 1 (March 1, 2013): 86. http://dx.doi.org/10.7146/math.scand.a-15235.

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Starting from an unpublished conjecture of Kalai and from a conjecture of Eisenbud, Green and Harris, we study several problems relating $h$-vectors of Cohen-Macaulay, flag simplicial complexes and face vectors of simplicial complexes.

9

Higashitani, Akihiro, and Kohji Yanagawa. "Non-level semi-standard graded Cohen–Macaulay domain with h -vector ( h 0 , h 1 , h 2 )." Journal of Pure and Applied Algebra 222, no. 1 (January 2018): 191–201. http://dx.doi.org/10.1016/j.jpaa.2017.03.011.

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10

Nast, Cynthia C., and Richard Glassock. "In remembrance of Arthur H. Cohen, MD (1942–2022)." Kidney International 102, no. 2 (August 2022): 218–19. http://dx.doi.org/10.1016/j.kint.2022.06.003.

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11

Porter, Roy. "The Scientific Revolution: A Historiographical Inquiry. H. Floris Cohen." Journal of Modern History 68, no. 3 (September 1996): 662–64. http://dx.doi.org/10.1086/245348.

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12

Letur, H. "Réponse de H. Letur à l'éditorial de J. Cohen." Gynécologie Obstétrique & Fertilité 35, no. 2 (February 2007): 168–69. http://dx.doi.org/10.1016/j.gyobfe.2006.12.014.

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13

Dumoff, Alan. "An Interview with Michael H. Cohen, J.D., M.B.A., M.F.A." Alternative and Complementary Therapies 10, no. 1 (February 2004): 46–51. http://dx.doi.org/10.1089/107628004772830410.

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14

Stan, Marius. "Response to H. Floris Cohen's essay review on Newtonian scholarship." British Journal for the History of Science 52, no. 2 (June 2019): 359–60. http://dx.doi.org/10.1017/s000708741900044x.

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15

Cordova, David, Jaime Munoz-Velazquez, Frania Mendoza Lua, Kathryn Fessler, Sydni Warner, Jorge Delva, Nicole Adelman, Angela Fernandez, and Jose Bauermeister. "Pilot Study of a Multilevel Mobile Health App for Substance Use, Sexual Risk Behaviors, and Testing for Sexually Transmitted Infections and HIV Among Youth: Randomized Controlled Trial." JMIR mHealth and uHealth 8, no. 3 (March 17, 2020): e16251. http://dx.doi.org/10.2196/16251.

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Background Preventing and reducing substance use disorders, sexually transmitted infections (STIs)/HIV, and teen pregnancy, and the associated risk behaviors (ie, substance use and sexual risk behaviors) among youth remain public health priorities in the United States. Equally important is improving the uptake of STI/HIV testing among the youth. Mobile health (mHealth) apps may be a solution to ameliorate these public health concerns; however, few mHealth preventive interventions have demonstrated efficacy in reducing substance use or sexual risk behaviors or improving the uptake of STI/HIV testing among the youth, particularly in clinic settings. Objective This small-scale study aimed to examine the feasibility of conducting a pilot randomized controlled trial (RCT). We evaluated the effects of Storytelling 4 Empowerment (S4E), relative to enhanced usual practice, on the potential mechanisms by which behavior change occurs, namely clinician-youth risk communication, prevention knowledge, and substance use and sexual risk refusal self-efficacy. We also assessed the ability to measure targeted outcomes of past 30-day substance use (ie, alcohol, tobacco, and other drug use), condomless sex, and alcohol or drug use before sex, as well as the uptake of STI/HIV testing. Methods Employing community-based participatory research principles, 50 youths aged 13 to 21 years were recruited from a youth-centered community health clinic in Southeast Michigan, randomized sequentially to either S4E or enhanced usual practice, and assessed at baseline, immediately postintervention, and 30 days postintervention. S4E consists of 3 modules, including alcohol and drug use, tobacco, and STI/HIV. Results Relative to youth in the enhanced usual practice group, S4E participants demonstrated higher youth-clinician risk communication (mean 3.22, SD 1.67) and increases in prevention knowledge (∆ score mean 0.36, SD 0.51) and self-efficacy (∆ score mean 0.16, SD 0.47). In addition, youth in the S4E group showed reductions in the proportions of past 30-day overall substance use (Cohen h=0.71, 95% CI 0.15 to 1.27), as well as past 30-day alcohol (Cohen h=0.71, 95% CI 0.15 to 1.27), tobacco (Cohen h=0.17, 95% CI −0.39 to 0.73), and drug use (Cohen h=1.28, 95% CI 0.72 to 1.84). The results also suggest a reduction in the proportion of youths who reported past 30-day condomless sex (Cohen h=0.18, 95% CI −0.38 to 0.74) and alcohol use before sex (Cohen h=0.44, 95% CI −0.12 to 1.00). Finally, the findings also demonstrated an increase in the proportion of youths who reported STI/HIV testing over time (Cohen h=0.16, 95% CI −0.39 to 0.72). Conclusions The findings suggest the feasibility of a small-scale pilot RCT. S4E demonstrated shifts in the hypothesized direction, reducing substance use, sexual risk behaviors, and improving the uptake of STI/HIV testing among youth in a clinic setting. The findings suggest that a larger RCT may be warranted. Trial Registration ClinicalTrails.gov NCT03855410, https://clinicaltrials.gov/ct2/show/NCT03855410.

16

Cioffi, F., and R. Di Gennaro. "When the positivity of the $$h$$ h -vector implies the Cohen-Macaulay property." Ricerche di Matematica 63, no. 2 (December 21, 2013): 195–209. http://dx.doi.org/10.1007/s11587-013-0174-4.

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17

Feingold, Mordechai. "Response to H. Floris Cohen's essay review on Newtonian scholarship." British Journal for the History of Science 52, no. 2 (June 2019): 353–57. http://dx.doi.org/10.1017/s0007087419000426.

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Long ago, George Sarton set down criteria for reviewers. In addition to insisting on the need to compose ‘faithful’ reviews, he cautioned against four types of unfit reviewers: the ‘egoist’, the ‘obscure’ reviewer, the one who is noncommittal, and the pedantic critic. Unfortunately, Cohen's review comes short on several counts. Cohen writes that he intends to examine what is ‘new’ in the three books he reviews, and whether the results therein contained are ‘worth learning’ (p. 687). Cohen denies being given to ‘misplaced hero worship’, insisting that his sole aim is to assess whether ‘scholarly novelty’ (p. 693) has been attained. Nevertheless, given his repeated rebuke of the authors under review for ‘failing to refer back to [Richard] Westfall's work’ on Newton – now nearly half a century old – it seems that he grounded his critique principally on Westfall's interpretation.

18

PATIL, D. P., and G. TAMONE. "ON THE COHEN–MACAULAYNESS OF SOME GRADED RINGS." Journal of Algebra and Its Applications 07, no. 01 (February 2008): 109–28. http://dx.doi.org/10.1142/s0219498808002692.

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Let (R,𝔪) be a 1-dimensional Cohen–Macaulay local ring of multiplicity e and embedding dimension ν ≥ 2. Let B denote the blowing-up of R along 𝔪 and let I be the conductor of R in B. Let x ∈ 𝔪 be a superficial element in 𝔪 of degree 1 and [Formula: see text], [Formula: see text]. We assume that the length [Formula: see text]. This class of local rings contains the class of 1-dimensional Gorenstein local rings (see 1.5). In Sec. 1, we prove that (see 1.6) if the associated graded ring G = gr 𝔪(R) is Cohen–Macaulay, then I ⊆ 𝔪s + xR, where s is the degree of the h-polynomial h R of R. In Sec. 2, we give necessary and sufficient conditions (see Corollaries 2.4, 2.5, 2.9 and Theorem 2.11) for the Cohen–Macaulayness of G. These conditions are numerical conditions on the h-polynomial h R, particularly on its coefficients and the degree in comparison with the difference e - ν. In Sec. 3, we give some conditions (see Propositions 3.2, 3.3 and Corollary 3.4) for the Gorensteinness of G. In Sec. 4, we give a characterization (see Proposition 4.3) of numerical semigroup rings which satisfy the condition [Formula: see text].

19

EHOLZER, WOLFGANG, and TOMOYOSHI IBUKIYAMA. "RANKIN–COHEN TYPE DIFFERENTIAL OPERATORS FOR SIEGEL MODULAR FORMS." International Journal of Mathematics 09, no. 04 (June 1998): 443–63. http://dx.doi.org/10.1142/s0129167x98000191.

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Let ℍn be the Siegel upper half space and let F and G be automorphic forms on ℍn of weights k and l, respectively. We give explicit examples of differential operators D acting on functions on ℍn × ℍn such that the restriction of [Formula: see text] to Z = Z1 = Z2 is again an automorphic form of weight k + l + v on ℍn. Since the elliptic case, i.e. n = 1, has already been studied some time ago by R. Rankin and H. Cohen we call such differential operators Rankin–Cohen type operators. We also discuss a generalisation of Rankin–Cohen type operators to vector valued differential operators.

20

Arrese Igor, Héctor Óscar. "La ley como acción de la autoconciencia moral en la ética de Hermann Cohen." Doxa. Cuadernos de Filosofía del Derecho, no. 33 (November 15, 2010): 503. http://dx.doi.org/10.14198/doxa2010.33.27.

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La ética de H. Cohen ha recibido la crítica de ser un mero formalismo abstracto, lo que implica una desconexión entre el individuo particular y la universalidad de la ley. En este trabajo intento mostrar que la filosofía moral de Cohen resiste estas críticas, porque el concepto de ley particular integra a la individualidad de cada ciudadano con la universalidad de la autoconciencia, que se expresa en el Estado.

21

Nordmann, Sophie. "Le peuple juif dans l'histoire ? H. Cohen et F. Rosenzweig." Pardès 45, no. 1 (2009): 235. http://dx.doi.org/10.3917/parde.045.0235.

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22

Capeill�res, Fabien. "Le cosmos de la culture. H. Cohen et E. Cassirer." Le Genre humain N�24-25, no. 1 (1992): 69. http://dx.doi.org/10.3917/lgh.024.0069.

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23

Schuster, John A. "Feature ReviewThe Scientific Revolution: A Historiographical Inquiry. H. Floris Cohen." Isis 88, no. 1 (March 1997): 118–21. http://dx.doi.org/10.1086/383630.

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24

Yanagawa, Kohji. "Castelnuovo's Lemma and h-vectors of Cohen-Macaulay homogeneous domains." Journal of Pure and Applied Algebra 105, no. 1 (November 1995): 107–16. http://dx.doi.org/10.1016/0022-4049(94)00139-1.

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25

Long, Pamela O. "The Scientific Revolution: A Historiographical Inquiry by H. Floris Cohen." Technology and Culture 37, no. 3 (July 1996): 619–21. http://dx.doi.org/10.1353/tech.1996.0047.

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26

Denizler, I. H., and R. Y. Sharp. "Co-Cohen-Macaulay Artinian modules over commutative rings." Glasgow Mathematical Journal 38, no. 3 (September 1996): 359–66. http://dx.doi.org/10.1017/s0017089500031797.

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In [7], Z. Tang and H. Zakeri introduced the concept of co-Cohen-Macaulay Artinian module over a quasi-local commutative ring R (with identity): a non-zero Artinian R-module A is said to be a co-Cohen-Macaulay module if and only if codepth A = dim A, where codepth A is the length of a maximalA-cosequence and dimA is the Krull dimension of A as defined by R. N. Roberts in [2]. Tang and Zakeriobtained several properties of co-Cohen-Macaulay Artinian R-modules, including a characterization of such modules by means of the modules of generalized fractions introduced by Zakeri and the present second author in [6]; this characterization is explained as follows.

27

Hibi, Takayuki, and Akiyoshi Tsuchiya. "Odd Cycles and Hilbert Functions of Their Toric Rings." Mathematics 8, no. 1 (December 20, 2019): 22. http://dx.doi.org/10.3390/math8010022.

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Studying Hilbert functions of concrete examples of normal toric rings, it is demonstrated that for each 1 ≤ s ≤ 5 , an O-sequence ( h 0 , h 1 , … , h 2 s − 1 ) ∈ Z ≥ 0 2 s satisfying the properties that (i) h 0 ≤ h 1 ≤ ⋯ ≤ h s − 1 , (ii) h 2 s − 1 = h 0 , h 2 s − 2 = h 1 and (iii) h 2 s − 1 − i = h i + ( − 1 ) i , 2 ≤ i ≤ s − 1 , can be the h-vector of a Cohen-Macaulay standard G-domain.

28

Cattaneo, Angelo. "The Visualization of Knowledge in Medieval and Early Modern Europe." Cromohs - Cyber Review of Modern Historiography 24 (June 8, 2022): 209–17. http://dx.doi.org/10.36253/cromohs-13520.

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Miyazaki, Mitsuhiro. "A Sequence of Cohen–Macaulay Standard Graded Domains Whose h-Vectors Have Exponentially Deep Flaws." AppliedMath 3, no. 2 (April 3, 2023): 305–15. http://dx.doi.org/10.3390/appliedmath3020017.

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30

Herzog, J., W. V. Vasconcelos, and R. Villarreal. "Ideals with sliding depth." Nagoya Mathematical Journal 99 (September 1985): 159–72. http://dx.doi.org/10.1017/s0027763000021553.

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We study here a class of ideals of a Cohen-Macaulay ring {R, m} somewhat intermediate between complete intersections and general Cohen-Macaulay ideals. Its definition, while a bit technical, rapidly leads to the development of its elementary properties. Let I = (x1 … xn) = (x) be an ideal of R and denote by H*(x) the homology of the ordinary Koszul complex K*(x) built on the sequence x. It often occurs that the depth of the module Hi i > 0, increases with i (as usual, we set depth (0) = ∞).

31

BELOV, V. N. "The Philosophy of Religion of H. Cohen and the Eastern Jewry." Personality.Culture.Society 21, no. 3-4 (2019): 43–48. http://dx.doi.org/10.30936/1606-951x-2019-21-3/4-43-48.

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32

Sokuler, Z. A. "The Concept of Virtue in Religious Philosophy of Hermann Cohen." RUDN Journal of Philosophy 23, no. 4 (December 15, 2019): 398–412. http://dx.doi.org/10.22363/2313-2302-2019-23-4-398-412.

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The concept of virtue was of great interest and importance for H. Cohen. In the interpretation of this concept in his latest work “Religion of reason from the sources of Judaism” the most important concepts of this work were brought in the focus: the specificity of definition of what is the religion of reason; understanding of the uniqueness of God; correlation; messianism. For Cohen, a single system of virtues presupposes a single and unique ethics and correlates with the idea of the unity of humanity. The last concept, in his opinion, maturated in the fold of monotheism. Humanity is one, because all people are creations of the unique God. “Religion of reason” treats of the common universal virtues. In the religion of reason, the idea of God and morality are inextricably linked. Cohen rejects metaphysical speculation about the nature of God, about the attributes of God inherent in himself. The religion of the mind speaks of God only in correlation with man. God is a moral ideal and reveals himself to man by giving him moral commandments. Morality connects man and God, and this connection is revealed in detail by Cohen in the theme of virtues. Understanding God as Truth is important for the disclosure of this topic. The corresponding virtue for a person is faithfulness to truth, or truthfulness. In addition to truthfulness in the usual sense, for Cohen, faithfulness to truth requires correct worship of God. The correlation culminates in the idea of messianism, which is interpreted by Cohen as an endless movement of a whole humanity to the social justice.

33

Do, Van-Kien, and Hong-Ngoc Nguyen. "The Koszulness of numerical semigroup rings of minimal multiplicity." HPU2 Journal of Science: Natural Sciences and Technology 2, no. 3 (December 29, 2023): 3–12. http://dx.doi.org/10.56764/hpu2.jos.2023.2.3.3-12.

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Let R = k [H] be a numerical semigroup ring over a field k and grm (R) is the associated graded ring of R. In this paper, we show that grm (R) is a Cohen-Macaulay ring, provided H has minimal multiplicity. As a consequence, we conclude that the numerical semigroup ring R = k [H] of minimal multiplicity is a Koszul ring, i.e., the residue field k has a grm (R) – linear free resolution.

34

GUERZHOY, P. "Quadratic congruences for Cohen–Eisenstein series." Glasgow Mathematical Journal 41, no. 1 (March 1999): 141–44. http://dx.doi.org/10.1017/s001708959997060x.

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The notion of quadratic congruences was introduced in the recently published paper [A. Balog, H. Darmon and K. Ono, Congruences for Fourier coefficients of half-integral weight modular forms and special values of L-functions, in Analytic Number Theory, Vol. 1, Progr. Math.138 (Birkhäuser, Boston, 1996), 105–128.]. In this note we present different, somewhat more conceptual proofs of several results from that paper. Our method allows us to refine the notion and to generalize the results quoted. Here we deal only with the quadratic congruences for Cohen–Eisenstein series. Similar phenomena exist for cusp forms of half-integral weight as well; however, as one would expect, in the case of Eisenstein series the argument is much simpler. In particular, we do not make use of techniques other than p-adic Mazur measure, whereas the consideration of cusp forms of half-integral weight involves a much more sophisticated construction. Moreover, in the case of Cohen–Eisenstein series we are able to obtain a full and exhaustive result. For these reasons we present the argument here.

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Ion, Cristian. "On the Hilbert function of vertex cover algebras of Cohen-Macaulay bipartite graphs." Annals of the ”Dunarea de Jos” University of Galati Fascicle II Mathematics Physics Theoretical Mechanics 45, no. 2 (December 12, 2022): 43–52. http://dx.doi.org/10.35219/ann-ugal-math-phys-mec.2022.2.02.

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We study the h−vector and the Hilbert function of the vertex cover algebra (A)G, introduced and first studied by J. Herzog, T. Hibi and N. V. Trung ([6]), for a special class of bipartite graphs, namely for Cohen-Macaulay bipartite graphs.

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Álvarez, J. N. Alonso, J. M. Fernández Vilaboa, R. González Rodríguez, and C. Soneira Calvo. "Cleft comodules over Hopf quasigroups." Communications in Contemporary Mathematics 17, no. 06 (October 29, 2015): 1550007. http://dx.doi.org/10.1142/s0219199715500078.

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In this paper, we provide necessary and sufficient conditions for a cleft right H-comodule algebra (A, ϱA) over a Hopf quasigroup H to be isomorphic as an algebra to the crossed product AH♯σAHH, where AH is the coinvariants subalgebra of A and σAH is a morphism between H ⊗ H and AH. As a consequence, we obtain the corresponding version in the nonassociative setting of the result given by Blattner, Cohen and Montgomery for projections of Hopf algebras with coalgebra splitting. Concrete examples satisfying the obtained conditions are provided.

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Ballico, E., and K. Yanagawa. "On the h-vector of a cohen-macaulay domain in positive characteristic." Communications in Algebra 26, no. 6 (January 1998): 1745–56. http://dx.doi.org/10.1080/00927879808826236.

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Mathai, Arak M., and Hans J. Haubold. "A Versatile Integral in Physics and Astronomy and Fox’s H-Function." Axioms 8, no. 4 (November 1, 2019): 122. http://dx.doi.org/10.3390/axioms8040122.

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This paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in physics and astronomy. Nuclear reaction rate probability integrals in nuclear physics, Krätzel integrals in applied mathematical analysis, inverse Gaussian distributions, generalized type-1, type-2, and gamma families of distributions in statistical distribution theory, Tsallis statistics and Beck–Cohen superstatistics in statistical mechanics, and Mathai’s pathway model are all shown to be connected to the integral under consideration. Representations of the integral in terms of Fox’s H-function are pointed out.

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Shevtsov, Alexandr. "Is ethics a logic? Sergei Rubinstein’s interpretation of Hermann Cohen’s ideas." SHS Web of Conferences 161 (2023): 05003. http://dx.doi.org/10.1051/shsconf/202316105003.

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In Sergei L. Rubinstein’s article “On the Philosophical System of H. Cohen” (1918), Hermann Cohen’s judgments on ethics and logic and their partly problematic relationship are considered. On the basis of historical and philosophical research into the epistemological views of Cohen I show the interaction between the ideas of Rubinstein and Neo-Kantianism. Common features of the following concepts are revealed: criticism, installation of logic, aspiration to prove philosophy a science with the help either of mathematics or the confirmation of its origin (Ursprung). Insofar as the problem of ethics plays a central role in his account, thanks to the inclusiveness in history, Rubinstein argues that ethics has the same objectivity as logic. The central problem of ethics both in Kant and in Cohen (and indeed in Rubinstein) lies in the nature of the person. In Rubinstein’s work, the answer to the main issue of ethics opens up the world of Ideas. The Ideas and logical content of consciousness constitute the person, just as in Cohen’s work ethics “generates” the person and the world. In this regard Rubinstein believed that Cohen had adopted a distinctive feature of the interpretation of ethics and freedom from Kant. Before presenting this background, an attempt is made to update the historical and philosophical value of the ideas of Rubinstein, clarifying the essence of the objects of ethics and logic.

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Conca, Aldo. "Symmetric ladders." Nagoya Mathematical Journal 136 (December 1994): 35–56. http://dx.doi.org/10.1017/s0027763000024958.

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In this paper we define and study ladder determinantal rings of a symmetric matrix of indeterminates. We show that they are Cohen-Macaulay domains. We give a combinatorial characterization of their h-vectors and we compute the a-invariant of the classical determinantal rings of a symmetric matrix of indeterminates.

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Goldstein, Eda G. "Parenthood: A Psychodynamic Perspective. Rebecca S. Cohen , Bertram S. Cohler , Sidney H. Weissman." Social Service Review 59, no. 4 (December 1985): 664–65. http://dx.doi.org/10.1086/644340.

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Gross, Guenter W. "Neural Control of Rhythmic Movements in Vertebrates.Avis H. Cohen , Serge Rossignol , Sten Grillner." Quarterly Review of Biology 64, no. 1 (March 1989): 93–94. http://dx.doi.org/10.1086/416195.

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Oren, Yehuda (Yady). "Dogmatism, Criticism, Divine Ideals: Rav A. I. Kook’s Concept of God in Light of H. Cohen." Naharaim 15, no. 2 (September 10, 2021): 153–77. http://dx.doi.org/10.1515/naha-2020-0006.

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Abstract This paper examines the claim that the two final articles of Rav Kook’s book Ikvei Hatzon were written as a response to a lecture given by Hermann Cohen. It first reviews Cohen’s lecture showing that, regarding the concept of God, Cohen argues for the compatibility of Judaism and Kantianism in denying the dogmatic-mythological preoccupation with the existence of God in favor of understanding God as the basis of morality. Second, it analyzes Kook’s articles, demonstrating that he accepts the compatibility of Judaism and Kantianism together with the denial of the dogmatic relation to God as a substance. Nevertheless, Kook is not satisfied with the critical view that denies the dogmatic relation to the substance altogether, since it formulates a merely negative relationship with God. Instead, he develops his concept of the Divine Ideals, which synthesizes the dogmatic preoccupation with substantiality and the critical denial of it. The Divine Ideals are the moral progression of man, through which man gradually becomes identical to God. Within the Divine Ideals, dogmatism becomes an emotional striving to be identical with God as a substance, while criticism is the intellectual negation of the possibility of such identity, which ensures that the process will continue indefinitely.

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AUSTIN, ELIZABETH. "Understanding Other Minds. Edited by S. Baron-Cohen, H. Tager-Flusberg and D. J. Cohen. (Pp. 530; £28.95.) Oxford University Press: Oxford. 2000." Psychological Medicine 31, no. 6 (July 31, 2001): 1135–38. http://dx.doi.org/10.1017/s0033291701214111.

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Nanduri, Ramakrishna. "Hilbert coefficients of Schubert varieties in Grassmannians." Journal of Algebra and Its Applications 14, no. 03 (November 7, 2014): 1550036. http://dx.doi.org/10.1142/s021949881550036x.

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In this paper, we give combinatorial formulas for the Hilbert coefficients, h-polynomial and the Cohen–Macaulay type of Schubert varieties in Grassmannians in terms of the posets associated with them. As a consequence, necessary conditions for a Schubert variety to be a complete intersection and combinatorial criteria are given for a Schubert variety to be Gorenstein and almost Gorenstein, respectively.

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Ganga, Deianira, B. Dilara Seker, Wadim Strielkowski, and Tuncay Bilecen. "Book Reviews." Migration Letters 12, no. 2 (May 1, 2015): 172–79. http://dx.doi.org/10.33182/ml.v12i2.251.

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Ambrosini, Maurizio. Irregular Migration and Invisible Welfare. Palgrave Macmillan, 2013. 256 pages (ISBN: 9781137314321).Cohen, Jeffrey H., and Ibrahim Sirkeci. Cultures of Migration: The Global Nature of Contemporary Mobility. Austin, TX: University of Texas Press, 2011. xiv + 165 pages. (ISBN: 9780292726857). Dedeoğlu, Saniye. Migrants, Work and Social Integration: Women's Labour in the Turkish Ethnic Economy, Palgrave Macmillan, 2014. 216 pages. (ISBN: 9781137371119)

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Shimmon, Karen. "Understanding Other Minds. Edited by S. Baron-Cohen, H. Tager-Flusberg, & D. Cohen. Oxford University Press, Oxford, 2000. pp. 530. £28·95 (pb)." Journal of Child Psychology and Psychiatry 42, no. 5 (July 2001): 699–702. http://dx.doi.org/10.1017/s0021963001246976.

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YANAGAWA, Kohji. "A note on the h-vector of a Cohen-Macaulay homogeneous domain." Japanese journal of mathematics. New series 23, no. 1 (1997): 179–86. http://dx.doi.org/10.4099/math1924.23.179.

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Norte, Grant E., Jay Hertel, Susan A. Saliba, David R. Diduch, and Joseph M. Hart. "Quadriceps Neuromuscular Function in Patients With Anterior Cruciate Ligament Reconstruction With or Without Knee Osteoarthritis: A Cross-Sectional Study." Journal of Athletic Training 53, no. 5 (May 1, 2018): 475–85. http://dx.doi.org/10.4085/1062-6050-102-17.

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Context: Central and peripheral neural adaptations have been identified after anterior cruciate ligament (ACL) injury and reconstruction (ACLR) and are hypothesized to contribute to posttraumatic muscle dysfunction. Limited evidence exists about the temporal nature of neuromuscular adaptations during early and late-term phases of recovery after ACLR, and no researchers have studied patients with posttraumatic osteoarthritis. Objective: To compare quadriceps neuromuscular function less than 2 years (early) and more than 2 years (late) after ACLR, including in patients who experienced posttraumatic knee osteoarthritis. Design: Cross-sectional study. Setting: Laboratory. Patients or Other Participants: A total of 72 patients after ACLR, consisting of 34 early (9.0 ± 4.3 months postsurgery), 30 late (70.5 ± 41.6 months postsurgery), and 8 with osteoarthritis (115.9 ± 110.0 months postsurgery), and 30 healthy control volunteers. Main Outcome Measure(s): Quadriceps function was measured bilaterally during a single visit to determine normalized Hoffmann reflex (H : M ratio), knee-extension maximal voluntary isometric contraction torque (Nm/kg), central activation ratio (%), fatigue index (% decline), and active motor threshold (%). Comparisons were made using 2-way analyses of variance to identify the effect of limb and group on each outcome measure. We calculated Cohen d effect sizes to assess the magnitude of difference between ACLR and matched control limbs for each group. Results: Compared with healthy control limbs, involved-limb maximal voluntary isometric contraction was lower among all patients after ACLR (P < .001, Cohen d values = −1.00 to −1.75). The central activation ratio (P < .001, Cohen d = −1.74) and fatigue index (P = .003, Cohen d = −0.95) were lower among patients only early after ACLR. The active motor threshold was higher among all patients after ACLR (P < .001, Cohen d values = −0.42 to −1.56). Conclusions: Neuromuscular impairments were present in patients early and late after ACLR, regardless of osteoarthritis status. Quadriceps strength and corticospinal excitability were impaired at each time point compared with values in healthy control individuals, suggesting the need to address cortical function early after ACLR.

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De Leon, Rodolfo Gomez Ponce, Luiz Francisco Baccaro, Gonzalo Rubio Schweizer, and Suzanne Jacob Serruya. "Analysis of the impact of COVID-19 pandemic on women´s care in an abortion situation in Latin America and the Caribbean." Cadernos Ibero-Americanos de Direito Sanitário 12, no. 4 (December 13, 2023): 14–32. http://dx.doi.org/10.17566/ciads.v12i4.1024.

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Objective: to understand the influence of the COVID-19 pandemic on aspects of quality of care provided to women in abortion situations in sentinel centers of the CLAP MUSA-Network (a multicenter network with international cooperation with the aim of encouraging good practices in Latin America and the Caribbean). Methods: cross-sectional study between January/2017 and December/2021 with women of any age admitted for abortion or miscarriage. We analyzed the total number of cases and the proportion of legal abortions. The dependent variables were complications and use of contraceptives after abortion. The independent variables were COVID-19 pandemic, clinical and sociodemographic data. Statistical analysis was carried out using linear regression, multiple Poisson regression, Cochran-Armitage, chi-square, Mann-Whitney and Cohen tests. Results: we analyzed data from 93689 women assisted in 12 sentinel centers of the CLAP MUSA-Network, 64.55% in the pre-pandemic period (NP) and 35.45% in the pandemic period (PP) (22.73% received post-abortion care and 77.27% legal abortion). We found no differences in the number of cases over the period, regardless of the legal context. We observed a significant increase in the proportion of legal abortions in liberal and moderate contexts. In NP, 46.46% of women underwent medical abortion, while 62.18% of women underwent medical abortion in PP (h-Cohen 0.32). We found no increase in the number of complications during PP. In NP, 79.12% started contraceptives after abortion, while in PP, 70.39% started contraceptives after abortion (h-Cohen 0.20). Conclusion: the COVID-19 pandemic was not associated with a decrease in the number of cases, a decrease in the proportion of legal interruptions, or an increase in complications in sentinel centers of the CLAP MUSA-Network. Submission: 30/04/23|Review: 08/11/23|Approval: 09/11/23