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Depth formula for modules of finite reducing projective dimension
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-11-20 DOI: 10.1007/s10231-024-01509-0
Olgur Celikbas, Toshinori Kobayashi, Brian Laverty, Hiroki Matsui
{"title":"Depth formula for modules of finite reducing projective dimension","authors":"Olgur Celikbas,&nbsp;Toshinori Kobayashi,&nbsp;Brian Laverty,&nbsp;Hiroki Matsui","doi":"10.1007/s10231-024-01509-0","DOIUrl":"10.1007/s10231-024-01509-0","url":null,"abstract":"<div><p>We prove that the depth formula holds for two finitely generated Tor-independent modules over Cohen–Macaulay local rings if one of the modules considered has finite reducing projective dimension (for example, if it has finite projective dimension, or the ring is a complete intersection). This generalizes a result of Bergh–Jorgensen which shows that the depth formula holds for two finitely generated Tor-independent modules over Cohen–Macaulay local rings if one of the modules considered has reducible complexity and certain additional conditions hold. Each module that has reducible complexity also has finite complexity and finite reducing projective dimension, but not necessarily vice versa. So a new advantage we have is that, unlike modules of reducible complexity, Betti numbers of modules of finite reducing projective dimension can grow exponentially.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"859 - 878"},"PeriodicalIF":1.0,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Needle orientation for temporomandibular joint arthrocentesis in Koreans. 韩国人颞下颌关节关节腔穿刺术的针头方向。
IF 2 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-11-01 Epub Date: 2022-03-09 DOI: 10.1080/08869634.2022.2047509
Atapol Yongvikul, Jae-Young Kim, Jeong-Kui Ku, Joon-Ho Jung, Jong-Ki Huh
{"title":"Needle orientation for temporomandibular joint arthrocentesis in Koreans.","authors":"Atapol Yongvikul, Jae-Young Kim, Jeong-Kui Ku, Joon-Ho Jung, Jong-Ki Huh","doi":"10.1080/08869634.2022.2047509","DOIUrl":"10.1080/08869634.2022.2047509","url":null,"abstract":"<p><strong>Objective: </strong>To investigate the highest opportunity skin puncture point and needle orientation according to facial asymmetry and classification.</p><p><strong>Methods: </strong>Computed tomography of 136 patients was analyzed. Horizontal and vertical angles and distances from the canthal-tragal line were investigated to determine the puncture point and needle's angle.</p><p><strong>Result: </strong>All patients' average points were 7.39 (±2.85) mm anterior to the tragus and 3.44 (±4.18) mm below the canthal-tragal line with an angle of 8.53 (±6.90)° anteriorly and 32.26 (±7.23)° superiorly. Regarding asymmetry, there was a statistical difference in horizontal angle, depth, and canthal-tragal distance between the deviated and non-deviated sides. Especially, vertical distances were 4.44 (±4.66) mm and 2.59 (±4.11) mm in the deviated and non-deviated sides, respectively (<i>p</i> < 0.001).</p><p><strong>Conclusion: </strong>In closed-mouth, the puncture point was closer to the tragus and lower than the conventional point. The point in the deviated side should be considered lower than the non-deviated side.</p>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"51 1","pages":"711-717"},"PeriodicalIF":2.0,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73993630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symplectic Grassmannians and cyclic quivers
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-10-14 DOI: 10.1007/s10231-024-01506-3
Evgeny Feigin, Martina Lanini, Matteo Micheli, Alexander Pütz
{"title":"Symplectic Grassmannians and cyclic quivers","authors":"Evgeny Feigin,&nbsp;Martina Lanini,&nbsp;Matteo Micheli,&nbsp;Alexander Pütz","doi":"10.1007/s10231-024-01506-3","DOIUrl":"10.1007/s10231-024-01506-3","url":null,"abstract":"<div><p>The goal of this paper is to extend the quiver Grassmannian description of certain degenerations of Grassmann varieties to the symplectic case. We introduce a symplectic version of quiver Grassmannians studied in our previous papers and prove a number of results on these projective algebraic varieties. First, we construct a cellular decomposition of the symplectic quiver Grassmannians in question and develop combinatorics needed to compute Euler characteristics and Poincaré polynomials. Second, we show that the number of irreducible components of our varieties coincides with the Euler characteristic of the classical symplectic Grassmannians. Third, we describe the automorphism groups of the underlying symplectic quiver representations and show that the cells are the orbits of this group. Lastly, we provide an embedding into the affine flag varieties for the affine symplectic group.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"793 - 814"},"PeriodicalIF":1.0,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01506-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New scattered subspaces in higher dimensions
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-10-07 DOI: 10.1007/s10231-024-01507-2
Daniele Bartoli, Alessandro Giannoni, Giuseppe Marino
{"title":"New scattered subspaces in higher dimensions","authors":"Daniele Bartoli,&nbsp;Alessandro Giannoni,&nbsp;Giuseppe Marino","doi":"10.1007/s10231-024-01507-2","DOIUrl":"10.1007/s10231-024-01507-2","url":null,"abstract":"<div><p>Over the past few decades, there has been extensive research on scattered subspaces, partly because of their link to MRD codes. These subspaces can be characterized using linearized polynomials over finite fields. Within this context, scattered sequences extend the concept of scattered polynomials and can be viewed as geometric equivalents of exceptional MRD codes. Up to now, only scattered sequences of orders one and two have been developed. However, this paper presents an infinite series of exceptional scattered sequences of any order beyond two which correspond to scattered subspaces that cannot be obtained as direct sum of scattered subspaces in smaller dimensions. The paper also addresses equivalence concerns within this framework.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"815 - 834"},"PeriodicalIF":1.0,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01507-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Fueter–Sce theorem for generalized partial-slice monogenic functions
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-09-30 DOI: 10.1007/s10231-024-01508-1
Zhenghua Xu, Irene Sabadini
{"title":"On the Fueter–Sce theorem for generalized partial-slice monogenic functions","authors":"Zhenghua Xu,&nbsp;Irene Sabadini","doi":"10.1007/s10231-024-01508-1","DOIUrl":"10.1007/s10231-024-01508-1","url":null,"abstract":"<div><p>In a recent paper, we introduced the concept of generalized partial-slice monogenic functions. The class of these functions includes both monogenic functions and slice monogenic functions with values in a Clifford algebra. In this paper, we establish a version of the Fueter–Sce theorem in this new setting, which allows to construct monogenic functions in higher dimensions starting from generalized partial-slice monogenic functions. We also prove that an alternative construction can be obtained by using the dual Radon transform. It turns out that these two constructions are closely related to the generalized CK-extension.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"835 - 857"},"PeriodicalIF":1.0,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01508-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On minimal homogeneous submanifolds of the hyperbolic space up to codimension two
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-09-28 DOI: 10.1007/s10231-024-01504-5
Felippe Guimarães, Joeri Van der Veken
{"title":"On minimal homogeneous submanifolds of the hyperbolic space up to codimension two","authors":"Felippe Guimarães,&nbsp;Joeri Van der Veken","doi":"10.1007/s10231-024-01504-5","DOIUrl":"10.1007/s10231-024-01504-5","url":null,"abstract":"<div><p>We show that a minimal homogeneous submanifold <span>(M^n)</span>, <span>(nge 5)</span>, of a hyperbolic space up to codimension two is totally geodesic.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"759 - 771"},"PeriodicalIF":1.0,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deformed solutions of the Yang–Baxter equation associated to dual weak braces
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-09-28 DOI: 10.1007/s10231-024-01502-7
Marzia Mazzotta, Bernard Rybołowicz, Paola Stefanelli
{"title":"Deformed solutions of the Yang–Baxter equation associated to dual weak braces","authors":"Marzia Mazzotta,&nbsp;Bernard Rybołowicz,&nbsp;Paola Stefanelli","doi":"10.1007/s10231-024-01502-7","DOIUrl":"10.1007/s10231-024-01502-7","url":null,"abstract":"<div><p>A recent method for acquiring new solutions of the Yang–Baxter equation involves deforming the classical solution associated with a skew brace. In this work, we demonstrate the applicability of this method to a dual weak brace <span>(left( S,+,circ right) )</span> and prove that all elements generating deformed solutions belong precisely to the set <span>(mathcal {D}_r(S)={z in S mid forall a,b in S , , (a+b) circ z = acirc z-z+b circ z})</span>, which we term the <i>distributor of </i><i>S</i>. We show it is a full inverse subsemigroup of <span>(left( S, circ right) )</span> and prove it is an ideal for certain classes of braces. Additionally, we express the distributor of a brace <i>S</i> in terms of the associativity of the operation <span>(cdot )</span>, with <span>(circ )</span> representing the circle or adjoint operation. In this context, <span>((mathcal {D}_r(S),+,cdot ))</span> constitutes a Jacobson radical ring contained within <i>S</i>. Furthermore, we explore parameters leading to non-equivalent solutions, emphasizing that even deformed solutions by idempotents may not be equivalent. Lastly, considering <i>S</i> as a strong semilattice <span>([Y, B_alpha , phi _{alpha ,beta }])</span> of skew braces <span>(B_alpha )</span>, we establish that a deformed solution forms a semilattice of solutions on each skew brace <span>(B_alpha )</span> if and only if the semilattice <i>Y</i> is bounded by an element 1 and the deforming element <i>z</i> lies in <span>(B_1)</span>.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"711 - 731"},"PeriodicalIF":1.0,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01502-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on local capacitary maximal functions
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-09-27 DOI: 10.1007/s10231-024-01505-4
Keng Hao Ooi
{"title":"A note on local capacitary maximal functions","authors":"Keng Hao Ooi","doi":"10.1007/s10231-024-01505-4","DOIUrl":"10.1007/s10231-024-01505-4","url":null,"abstract":"<div><p>We introduce a type of local Hardy-Littlewood maximal function defined in terms of Choquet integrals associated with Bessel capacities. The weak and strong types estimates will be justified. As an application, we obtain a capacitary type of Lebesgue differentiation theorem. \u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"773 - 791"},"PeriodicalIF":1.0,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new Adams’ inequality involving the ( (frac{N}{2},p)-)Bilaplacian operators and applications to some biharmonic nonlocal equation
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-09-23 DOI: 10.1007/s10231-024-01503-6
Sami Aouaoui
{"title":"A new Adams’ inequality involving the ( (frac{N}{2},p)-)Bilaplacian operators and applications to some biharmonic nonlocal equation","authors":"Sami Aouaoui","doi":"10.1007/s10231-024-01503-6","DOIUrl":"10.1007/s10231-024-01503-6","url":null,"abstract":"<div><p>In this paper, we prove some new inequality of Adams’ type for some new higher order Sobolev space whose norm is a combination of the norms of the <span>( frac{N}{2}-)</span>Bilaplacian and the <span>( p-)</span>Bilaplacian with <span>( p &lt; frac{N}{2} )</span> in the whole euclidean space <span>( mathbb {R}^N, N ge 4. )</span> The inequality proved is completely new. Next, an improvement of this inequality, inspired by the concentration-compactness principle of P. Lions, is also provided. This improvement is not trivial and its proof needs some new sophisticated tools. Finally, using this inequality, we treat in the last part of this work, some biharmonic elliptic quasilinear equation involving <span>( (frac{N}{2},p)-)</span>Bilaplacian operators and where the nonlinearities enjoy an exponential growth condition at infinity.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"733 - 757"},"PeriodicalIF":1.0,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stable solutions to fractional semilinear equations: uniqueness, classification, and approximation results 分数半线性方程的稳定解：唯一性、分类和近似结果
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-09-17 DOI: 10.1007/s10231-024-01497-1
Tomás Sanz-Perela
{"title":"Stable solutions to fractional semilinear equations: uniqueness, classification, and approximation results","authors":"Tomás Sanz-Perela","doi":"10.1007/s10231-024-01497-1","DOIUrl":"10.1007/s10231-024-01497-1","url":null,"abstract":"<div><p>We study stable solutions to fractional semilinear equations <span>((-Delta )^s u = f(u))</span> in <span>(Omega subset {mathbb {R}}^n)</span>, for convex nonlinearities <i>f</i>, and under the Dirichlet exterior condition <span>(u=g)</span> in <span>({mathbb {R}}^n {setminus } Omega)</span> with general <i>g</i>. We establish a uniqueness and a classification result, and we show that weak (energy) stable solutions can be approximated by a sequence of bounded (and hence regular) stable solutions to similar problems. As an application of our results, we establish the interior regularity of weak (energy) stable solutions to the problem for the half-Laplacian in dimensions <span>(1 leqslant n leqslant 4)</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"593 - 624"},"PeriodicalIF":1.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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