861 results on '"ramification"'
Search Results
2. On [formula omitted] and [formula omitted] number fields ramified at a single prime.
- Author
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Ogasawara, Takeshi and Schaeffer, George J.
- Subjects
- *
MODULAR forms , *POLYNOMIALS - Abstract
We present new examples of PGL 2 (F 7) and PSL 2 (F 7) number fields ramified at a single prime. To find these number fields we employ the following methods: (i) Specializing a modification of Malle's PGL 2 (F 7) polynomial, (ii) Modular method: computation of Katz modular forms of weight one over F ‾ 7 with prime level, and (iii) Searching for polynomials with prescribed ramification. Method (i) quickly generates many PGL 2 (F 7) number fields unramified at 7 including those fields ramified at only a single prime. Method (ii) can be used to show the existence of PGL 2 (F 7) or PSL 2 (F 7) number fields ramified only at primes that divide the level; we can then use method (iii) to find polynomials for those fields in many cases. [ABSTRACT FROM AUTHOR]
- Published
- 2025
- Full Text
- View/download PDF
3. Modified defect relation for Gauss maps of minimal surfaces with hypersurfaces of projective varieties in the subgeneral position.
- Author
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Quang, Si Duc
- Subjects
- *
GAUSS maps , *HOLOMORPHIC functions , *PROJECTIVE spaces , *HYPERSURFACES , *HYPERPLANES , *MINIMAL surfaces - Abstract
In this paper, we establish some modified defect relations for the Gauss map g$g$ of a complete minimal surface S⊂Rm$S\subset \mathbb {R}^m$ into a k$k$‐dimension projective subvariety V⊂Pn(C)(n=m−1)$V\subset \mathbb {P}^n(\mathbb {C})\ (n=m-1)$ with hypersurfaces Q1,...,Qq$Q_1,\ldots,Q_q$ of Pn(C)$\mathbb {P}^n(\mathbb {C})$ in N$N$‐subgeneral position with respect to V(N≥k)$V\ (N\ge k)$. In particular, we give the upper bound for the number q$q$ if the image g(S)$g(S)$ intersects each hypersurface Q1,...,Qq$Q_1,\ldots,Q_q$ a finite number of times and g$g$ is nondegenerate over Id(V)$I_d(V)$, where d=lcm(degQ1,...,degQq)$d=\text{lcm}(\deg Q_1,\ldots,\deg Q_q)$, that is, the image of g$g$ is not contained in any hypersurface Q$Q$ of degree d$d$ with V⊄Q$V\not\subset Q$. Our results extend and generalize the previous results for the case of the Gauss map and hyperplanes in a projective space. The results and the method of this paper have been applied by some authors to study the unicity problem of the Gauss maps sharing families of hypersurfaces. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
4. Jacobian and Polar Curves of Singular Foliations
- Author
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Corral, Nuria, Cano, Felipe, editor, Cisneros-Molina, José Luis, editor, Dũng Tráng, Lê, editor, and Seade, José, editor
- Published
- 2024
- Full Text
- View/download PDF
5. Value distribution properties for Gauss maps of immersed harmonic surfaces ramified over hypersurfaces
- Author
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Lu, Canhui and Chen, Xingdi
- Published
- 2024
- Full Text
- View/download PDF
6. Ramification of p-power torsion points of formal groups
- Author
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Iovita, Adrian, Morrow, Jackson S., and Zaharescu, Alexandru
- Published
- 2024
- Full Text
- View/download PDF
7. Comparison of Contrast-Enhanced 3D Imaging with 2D Imaging in the Evaluation of Perianal Fistula at 3T: A Prospective Observational Study
- Author
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Abdulla KV, Venkatesh Kasi Arunachalam, Haleema Sherene, Vijayakumaran Ethiraju, Rupa Ranganathan, Gowtham SM, Sriman Rajasekaran, Pankaj Mehta, and Mathew Cherian
- Subjects
3 Tesla ,3D sequence ,abscess ,perianal fistula ,ramification ,VIBE ,Medical physics. Medical radiology. Nuclear medicine ,R895-920 - Abstract
Introduction Perianal fistula and its recurrence is a challenging entity for surgeons. It is a well-establi1shed fact that magnetic resonance imaging (MRI) findings influence surgical procedures and reduce the rate of recurrence. In this study, we assessed the contrast-enhanced (CE) three dimensional T1 sequences [sampling perfection with application optimized contrast using different flip angle evolution (SPACE) and volumetric interpolated breath-hold examination (VIBE)] in a 3T MRI system to evaluate perianal fistulas and compared them with two-dimensional (2D) sequences.
- Published
- 2024
- Full Text
- View/download PDF
8. A characterization of ramification groups via jet algebras
- Author
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Marques, Sophie and Pagano, Luigi
- Published
- 2024
- Full Text
- View/download PDF
9. Comparison of Contrast-Enhanced 3D Imaging with 2D Imaging in the Evaluation of Perianal Fistula at 3T: A Prospective Observational Study.
- Author
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KV, Abdulla, Arunachalam, Venkatesh Kasi, Sherene, Haleema, Ethiraju, Vijayakumaran, Ranganathan, Rupa, SM, Gowtham, Rajasekaran, Sriman, Mehta, Pankaj, and Cherian, Mathew
- Subjects
- *
ANAL fistula , *THREE-dimensional imaging , *SCIENTIFIC observation , *DESCRIPTIVE statistics , *LONGITUDINAL method , *COMPARATIVE studies - Abstract
Introduction Perianal fistula and its recurrence is a challenging entity for surgeons. It is a well-establi1shed fact that magnetic resonance imaging (MRI) findings influence surgical procedures and reduce the rate of recurrence. In this study, we assessed the contrast-enhanced (CE) three dimensional T1 sequences [sampling perfection with application optimized contrast using different flip angle evolution (SPACE) and volumetric interpolated breath-hold examination (VIBE)] in a 3T MRI system to evaluate perianal fistulas and compared them with two-dimensional (2D) sequences. Materials and Methods Forty-four patients (mean age, 38.8 ± 15.3 [standard deviation]; 32 males, 12 females) with perianal fistula were included in this prospective study. The patients underwent conventional noncontrast, 2D sequences, diffusion-weighted imaging, followed by postcontrast, 2D T1 images in both axial and coronal planes, and 3D sequences at 3T. Acquisition times were recorded for each sequence. Each postcontrast sequence was evaluated in terms of image quality, presence of artifacts, fistula type, presence of an abscess, visibility, and number of internal orifices. The surgical findings were considered the gold standard. The imaging findings were compared with the surgical findings. Results In all three sequences, the fistula type and abscess were identified correctly in all patients. The sensitivity value for identification of ramifications utilizing CE 3D T1 VIBE sequence, CE 3D T1 SPACE, and CE 2D T1 images was 100, 86, and 36%, respectively. The number of internal orifices was identified by the CE 3D T1 VIBE and CE 3D T1 SPACE sequences in 100 and 92% of patients, respectively. CE 2D T1 images correctly identified internal orifices in 80% of patients. The overall scan time for each 3D sequence was shorter than for the combined postcontrast 2D sequences. Conclusion CE 3D T1 SPACE and CE 3D T1 VIBE sequences outperformed conventional CE 2D sequences in the evaluation of perianal fistulas in terms of visibility and the number of internal orifices with a shorter scanning time. Among the 3D sequences, CE 3D T1 VIBE is slightly superior to CE 3D T1 SPACE sequence. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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10. Sedum survival and ramification patterns under different pedoclimatic conditions
- Author
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A.P. Cotoz, V.S. Dan, T.M. Gocan, I. Andreica, S. Rózsa, and M. Cantor
- Subjects
succulent ,stress tolerance ,ramification ,traditional motifs ,substrates ,Plant culture ,SB1-1110 - Abstract
This article explores the use of Sedum species in landscape design, focusing on their adaptability to different pedoclimatic conditions and their ability to thrive in conditions of neglect. The article discusses the importance of understanding a plant's place of origin and natural habitat when considering its cultivation in a different area and the benefits and drawbacks associated with different types of substrates. Sedums are identified as an excellent choice for those who want to enjoy the aesthetic value of plants without the hassle of regular upkeep. The study investigates the growth and survival patterns of three Sedum cultivars in different growth media without additional watering or fertilization. The findings have the potential to provide insights into landscaping solutions and the evolution of these succulent species in arduous conditions. The study also explores Romanian identity and tradition by incorporating traditional motifs and patterns as mosaics into the landscape, creating a new style of landscaping. In addition to our main objective, we were interested in displaying an intricate landscape design to further illustrate the negative visual impact an un-cared-for outdoor environment can have.
- Published
- 2023
- Full Text
- View/download PDF
11. Height of algebraic units under splitting conditions.
- Author
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Prasad, Gorekh
- Subjects
PRIME ideals ,RATIONAL points (Geometry) - Abstract
Let α be a non-zero algebraic unit which is not a root of unity and K be a number field of degree d over Q . In this paper, we prove the following: Let P be a prime ideal of O K which lies above a rational odd prime p such that P O K (α) = P 1 e 1 P 2 e 2 ⋯ P g e g , where max 1 ≤ i ≤ g { e i } ≤ p and e 1 + ⋯ + e g = [ K (α) : K ]. Then h (α) ≥ c , where c > 0 is an effectively computable constant depending only on p and [ K : Q ] = d. This generalizes a result of Petsche. Also, we prove the following: Let P be a prime ideal of O K which lies above 2 such that P O K (α) = P 1 e 1 P 2 e 2 ⋯ P r e r , where e 1 + ⋯ + e r = [ K (α) : K ]. Then M (α) ≥ C (K) , where C (K) > 1 is a constant which depends only on [ K : Q ] = d. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
12. VFR TRAVEL AND COVID-19 IMPACTS: THE SOUTH AFRICAN EXPERIENCE
- Author
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Christian M. ROGERSON and Jayne M. ROGERSON
- Subjects
vfr travel ,covid-19 impacts ,ramification ,africa tourism ,south africa ,Geography. Anthropology. Recreation ,Geography (General) ,G1-922 - Abstract
COVID-19 had major negative consequences globally for travel for visits to friends and relatives (VFR), which is an under-researched segment of tourism. This paper responds to the need for extended research on VFR travel by examining the impacts of COVID-19 on the VFR sector and its spatial imprint in South Africa. VFR travel sector was second only to business travel in terms of the negative impacts of COVID-19 restrictions imposed in South Africa. An uneven geography is observed of the impact of COVID-19 on VFR travel mobilities. Using data on VFR trips and bednights the analysis discloses the greatest absolute declines in VFR travel occurred in South Africa’s major metropolitan areas. By contrast, in terms of the relative decline and local impacts for destinations of the COVID-19 hollowing out of VFR travel a different pattern emerges. The worst affected spaces were remote, mainly rural localities which are in South Africa’s poorest and most economically distressed areas.
- Published
- 2023
- Full Text
- View/download PDF
13. A Brief Survey of Paradigmatic Fractals from a Topological Perspective.
- Author
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Patiño Ortiz, Julián, Patiño Ortiz, Miguel, Martínez-Cruz, Miguel-Ángel, and Balankin, Alexander S.
- Subjects
- *
FRACTAL dimensions , *MATHEMATICAL connectedness , *FRACTALS - Abstract
The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity) and the notion of a fractal dimension D which exceeds the topological dimension d . In this regard, we point out that the constitutive inequality D > d can have either a geometric or topological origin, or both. The main topological features of fractals are their connectedness, connectivity, ramification, and loopiness. We argue that these features can be specified by six basic dimension numbers which are generally independent from each other. However, for many kinds of fractals, the number of independent dimensions may be reduced due to the peculiarities of specific kinds of fractals. Accordingly, we survey the paradigmatic fractals from a topological perspective. Some challenging points are outlined. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
14. Aspects of p-adic computation
- Author
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Doris, Christopher and Dokchitser, Tim
- Subjects
510 ,mathematics ,number theory ,p-adic ,local fields ,ramification ,computation - Abstract
We present a collection of new algorithms and approaches to several aspects of p-adic computation including: • computing the Galois group of a polynomial defined over a p-adic field; • computing the conductor of a 2-adic hyperelliptic curve of genus 2; • representing p-adic numbers exactly using lazy arithmetic; and • finding the roots of a system of polynomials in several variables over a p-adic field. In all cases, these algorithms are new or improve significantly on the previous state of the art. Most are implemented in the Magma computer algebra system, with source code freely available on the author's website. We have used these to prove the conductors of all genus 2 curves in the L-functions and modular forms database (LMFDB), which were previously conjectural, and have verified the Galois groups in the local fields database. We have also produced tables of previously unknown Galois groups, also available on the author's website.
- Published
- 2019
15. Ramified structure.
- Author
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Uzquiano, Gabriel
- Subjects
- *
AXIOMS , *TYPE theory , *PARADOX , *GRAMMAR , *ABBREVIATIONS - Abstract
The Russell–Myhill theorem threatens a familiar structured conception of propositions according to which two sentences express the same proposition only if they share the same syntactic structure and their corresponding syntactic constituents share the same semantic value. Given the role of the principle of universal instantiation in the derivation of the theorem in simple type theory, one may hope to rehabilitate the core of the structured view of propositions in ramified type theory, where the principle is systematically restricted. We suggest otherwise. The ramified core of the structured theory of propositions remains inconsistent in ramified type theory augmented with axioms of reducibility. This is significant because reducibility has been thought to be perfectly consistent with the ramified approach to the intensional antinomies. Nor is the addition of reducibility to ramified type theory sufficient to restore other intensional puzzles such as Prior's paradox or Kripke's puzzle about time and thought. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
16. THE GALOIS GROUP OF Xp² + aX + a.
- Author
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MOKHTARI, SOUFYANE and BENSEBA, BOUALEM
- Subjects
PRIME numbers ,ODD numbers ,FINITE simple groups ,NEWTON diagrams - Abstract
Let p be an odd prime number, and a be an integer divisible by p exactly once. We prove that the Galois group G of the trinomial X
p ² + aX + a over the field Q of rational number, is either the full symmetric group Sp ², or AGL(1, p²) ≤ G ≤ AGL(2, p). And we show that G ≃ Sp ², except possibly when p ≡ 1 (mod 8), and each prime divisor q of p + 1 satisfies q ̸≡ -1 (mod 4), and p divides the l-adic valuation vl(a) of a for each prime divisor l of a/p. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
17. Lehmer's problem and splitting of rational primes in number fields.
- Author
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Prasad, G. and Kumar, K. Senthil
- Subjects
- *
RATIONAL numbers , *PRIME numbers , *INTEGERS , *IDEALS (Algebra) , *PRIME ideals - Abstract
Let α be a non-zero algebraic integer of degree d which is not a root of unity. We prove that, if there exists an odd prime p with either (1) p ≤ d + 1 and p O Q (α) = P 1 P 2 ⋯ P d where P 1 , ... , P d are distinct prime ideals of O Q (α) , or (2) p ≤ d and p O Q (α) = P 1 e 1 P 2 e 2 ⋯ P g e g , where max 1 ≤ i ≤ g { e i } ≤ p and ∑ i = 1 g e i = d , then M (α) ≥ p / 2. We also prove that if the residual degrees of primes in O Q (α) which are lying above 2 are 1 , then M (α) ≥ 2 1 / 4 . This generalizes a result of Garza. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
18. VFR TRAVEL AND COVID-19 IMPACTS: THE SOUTH AFRICAN EXPERIENCE.
- Author
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ROGERSON, Christian M. and ROGERSON, Jayne M.
- Subjects
COVID-19 ,METROPOLITAN areas ,BUSINESS travel - Abstract
COVID-19 had major negative consequences globally for travel for visits to friends and relatives (VFR), which is an under-researched segment of tourism. This paper responds to the need for extended research on VFR travel by examining the impacts of COVID-19 on the VFR sector and its spatial imprint in South Africa. VFR travel sector was second only to business travel in terms of the negative impacts of COVID-19 restrictions imposed in South Africa. An uneven geography is observed of the impact of COVID-19 on VFR travel mobilities. Using data on VFR trips and bednights the analysis discloses the greatest absolute declines in VFR travel occurred in South Africa's major metropolitan areas. By contrast, in terms of the relative decline and local impacts for destinations of the COVID-19 hollowing out of VFR travel a different pattern emerges. The worst affected spaces were remote, mainly rural localities which are in South Africa's poorest and most economically distressed areas. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
19. Essential finite generation of extensions of valuation rings.
- Author
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Datta, Rankeya
- Subjects
- *
VALUATION , *CHARACTERISTIC functions , *FINITE, The - Abstract
Given a generically finite local extension of valuation rings V⊂W$V \subset W$, the question of whether W is the localization of a finitely generated V‐algebra is significant for approaches to the problem of local uniformization of valuations using ramification theory. Hagen Knaf proposed a characterization of when W is essentially of finite type over V in terms of classical invariants of the extension of associated valuations. Knaf's conjecture has been verified in important special cases by Cutkosky and Novacoski using local uniformization of Abhyankar valuations and resolution of singularities of excellent surfaces in arbitrary characteristic, and by Cutkosky for valuation rings of function fields of characteristic 0 using embedded resolution of singularities. In this paper, we prove Knaf's conjecture in full generality. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
20. Pólya fields and Kuroda/Kubota unit formula.
- Author
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Tougma, Charles Wend-Waoga
- Subjects
- *
MATHEMATICS , *INTEGERS , *POLYNOMIALS , *COHOMOLOGY theory , *PRIME numbers - Abstract
Let K be a number field. The Pólya field concept is used to know when the module of integer-valued polynomials over the ring of integers K of K has a regular basis. In [C. W.-W. Tougma, Some questions on biquadratic Pólya fields, J. Number Theory 229 (2021) 386–398], the author used cohomological results from [C. B. Setzer, Units over totally real C 2 × C 2 fields, J. Number Theory 12 (1980) 160–175] to answer questions raised in [A. Leriche, Pólya fields, Pólya groups and Pólya extensions: a question of capitulation, J. Théor. Nr. Bordx. 23 (2011) 235–249; A. Leriche, Cubic, quartic and sextic Pólya fields, J. Number Theory 133 (2013) 59–71] on biquadratic Pólya fields. Here we first prove that number fields were omitted from the list of exceptional fields cited in [A. Leriche, Pólya fields, Pólya groups and Pólya extensions: a question of capitulation, J. Théor. Nr. Bordx. 23 (2011) 235–249; A. Leriche, Cubic, quartic and sextic Pólya fields, J. Number Theory 133 (2013) 59–71]. We therefore identify new biquadratic Pólya fields, where the prime number 2 is totally ramified. This result corrects and completes some others on the literature. On the other hand, we show that the main results of [C. W.-W. Tougma, Some questions on biquadratic Pólya fields, J. Number Theory 229 (2021) 386–398] and this paper can be proved with a single method using Kuroda/Kubota's unit formula without cohomological results of [C. B. Setzer, Units over totally real C 2 × C 2 fields, J. Number Theory 12 (1980) 160–175]. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
21. Algorithmically Broad Languages for Polynomial Time and Space
- Author
-
Leivant, Daniel, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Silva, Alexandra, editor, Wassermann, Renata, editor, and de Queiroz, Ruy, editor
- Published
- 2021
- Full Text
- View/download PDF
22. Pólya fields and Kuroda/Kubota unit formula
- Author
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Charles Wend-Waoga Tougma
- Subjects
Regular basis ,principal ideals ,ramification ,group of units ,norm equation ,Mathematics ,QA1-939 - Abstract
Let K be a number field. The Pólya field concept is used to know when the module of integer-valued polynomials over the ring of integers [Formula: see text] of K has a regular basis. In [C. W.-W. Tougma, Some questions on biquadratic Pólya fields, J. Number Theory 229 (2021) 386–398], the author used cohomological results from [C. B. Setzer, Units over totally real [Formula: see text] fields, J. Number Theory 12 (1980) 160–175] to answer questions raised in [A. Leriche, Pólya fields, Pólya groups and Pólya extensions: a question of capitulation, J. Théor. Nr. Bordx. 23 (2011) 235–249; A. Leriche, Cubic, quartic and sextic Pólya fields, J. Number Theory 133 (2013) 59–71] on biquadratic Pólya fields. Here we first prove that number fields were omitted from the list of exceptional fields cited in [A. Leriche, Pólya fields, Pólya groups and Pólya extensions: a question of capitulation, J. Théor. Nr. Bordx. 23 (2011) 235–249; A. Leriche, Cubic, quartic and sextic Pólya fields, J. Number Theory 133 (2013) 59–71]. We therefore identify new biquadratic Pólya fields, where the prime number 2 is totally ramified. This result corrects and completes some others on the literature. On the other hand, we show that the main results of [C. W.-W. Tougma, Some questions on biquadratic Pólya fields, J. Number Theory 229 (2021) 386–398] and this paper can be proved with a single method using Kuroda/Kubota’s unit formula without cohomological results of [C. B. Setzer, Units over totally real [Formula: see text] fields, J. Number Theory 12 (1980) 160–175].
- Published
- 2023
- Full Text
- View/download PDF
23. Intraparotid Branching Pattern of Facial Nerve-A Cadaveric Study from Tamil Nadu, India.
- Author
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SUGANYA, S. and GOVINDARAJAN, AMUDHA
- Subjects
- *
MEDICAL sciences , *FACIAL nerve , *PAROTID glands , *FACIAL expression , *STATISTICAL software - Abstract
Introduction: Facial Nerve (FN) is the main motor nerve of muscles of facial expression. As it courses, within the parotid gland, the FN divides into divisions and then into terminal branches. Various surgical procedures of this region may inadvertently injure the FN owing to its variant branching pattern, resulting in facial asymmetry. Aim: To analyse the branching pattern of FN in the parotid region of Indian origin. Materials and Methods: This was a descriptive, cross-sectional study done on 50 embalmed cranial halves, in the Department of Anatomy, PSG Institute of Medical Sciences and Research, Coimbatore, Tamil Nadu, India from October 2020 to March 2022. Well-embalmed and preserved adult cadavers irrespective of age, sex and side were included. After piece meal dissection of the parotid gland, the Facial Nerve Trunk (FNT) was identified and its branching pattern studied and classified according to Davis RA et al., classification. The data thus, obtained was analysed using statistical software Statistical Package for the Social Sciences (SPSS) 21.0. Results: The FNT bifurcated in 98% and trifurcated in 2% specimens. The branching pattern of FN based on Davis RA et al., system showed a frequency as follows: Type I: 0%, Type II: 8%, Type III: 26%, Type IV: 16%, Type V: 48% and Type VI: 2%. Conclusion: Type V branching pattern showed the highest frequency. Results inferred from this study might help surgeons in anticipating the variant course, branching and interconnections of the FNT in the parotid region and thus, may aid in minimising iatrogenic nerve injuries to avoid unnecessary facial disabilities. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
24. Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$
- Author
-
Julio Pérez-Hernández and Mario Pineda-Ruelas
- Subjects
ramification ,cyclic quartic field ,discriminant ,index ,Mathematics ,QA1-939 - Abstract
If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prime of the form $4+n^2$, we give appropriate generators of $K$ to obtain the explicit factorization of the ideal $q{\mathcal O}_K$, where $q$ is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals.
- Published
- 2021
- Full Text
- View/download PDF
25. AFRICAN TOURISM IN UNCERTAIN TIMES: COVID-19 RESEARCH PROGRESS
- Author
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Christian M. ROGERSON and Jayne M. ROGERSON
- Subjects
covid-19 ,tourism in change ,africa ,ramification ,adaptation ,transformation ,global south ,Geography. Anthropology. Recreation ,Geography (General) ,G1-922 - Abstract
COVID-19 is a trigger event which is changing the complexion of African tourism and the directions of African tourism research. This article offers an overview and commentary on the state of African research produced during the uncertain times of 2020-2021 in specific response to the immediate impacts and changes which have been catalysed by the pandemic. The article is a progress report to capture and profile the body of focussed contributions on COVID-19 and tourism which have appeared for sub-Saharan Africa. Further, it is a contribution towards strengthening our understanding of tourism and change in the Global South. Overall, the discussion serves to highlight an emerging African scholarship which is engaged on a range of issues around three core themes of ramification, adaptation and transformation.
- Published
- 2021
- Full Text
- View/download PDF
26. Intraparotid Branching Pattern of Facial Nerve- A Cadaveric Study from Tamil Nadu, India
- Author
-
S Suganya and Amudha Govindarajan
- Subjects
bifurcation ,facial palsy ,nerve injury ,ramification ,variation ,Medicine - Abstract
Introduction: Facial Nerve (FN) is the main motor nerve of muscles of facial expression. As it courses, within the parotid gland, the FN divides into divisions and then into terminal branches. Various surgical procedures of this region may inadvertently injure the FN owing to its variant branching pattern, resulting in facial asymmetry. Aim: To analyse the branching pattern of FN in the parotid region of Indian origin. Materials and Methods: This was a descriptive, cross-sectional study done on 50 embalmed cranial halves, in the Department of Anatomy, PSG Institute of Medical Sciences and Research, Coimbatore, Tamil Nadu, India from October 2020 to March 2022. Well-embalmed and preserved adult cadavers irrespective of age, sex and side were included. After piece meal dissection of the parotid gland, the Facial Nerve Trunk (FNT) was identified and its branching pattern studied and classified according to Davis RA et al., classification. The data thus, obtained was analysed using statistical software Statistical Package for the Social Sciences (SPSS) 21.0. Results: The FNT bifurcated in 98% and trifurcated in 2% specimens. The branching pattern of FN based on Davis RA et al., system showed a frequency as follows: Type I: 0%, Type II: 8%, Type III: 26%, Type IV: 16%, Type V: 48% and Type VI: 2%. Conclusion: Type V branching pattern showed the highest frequency. Results inferred from this study might help surgeons in anticipating the variant course, branching and interconnections of the FNT in the parotid region and thus, may aid in minimising iatrogenic nerve injuries to avoid unnecessary facial disabilities.
- Published
- 2022
- Full Text
- View/download PDF
27. A Brief Survey of Paradigmatic Fractals from a Topological Perspective
- Author
-
Julián Patiño Ortiz, Miguel Patiño Ortiz, Miguel-Ángel Martínez-Cruz, and Alexander S. Balankin
- Subjects
dimension numbers ,connectedness ,connectivity ,ramification ,loopiness ,degrees of freedom ,Thermodynamics ,QC310.15-319 ,Mathematics ,QA1-939 ,Analysis ,QA299.6-433 - Abstract
The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity) and the notion of a fractal dimension D which exceeds the topological dimension d. In this regard, we point out that the constitutive inequality D>d can have either a geometric or topological origin, or both. The main topological features of fractals are their connectedness, connectivity, ramification, and loopiness. We argue that these features can be specified by six basic dimension numbers which are generally independent from each other. However, for many kinds of fractals, the number of independent dimensions may be reduced due to the peculiarities of specific kinds of fractals. Accordingly, we survey the paradigmatic fractals from a topological perspective. Some challenging points are outlined.
- Published
- 2023
- Full Text
- View/download PDF
28. Discriminant-stability in p-adic Lie towers of number fields.
- Author
-
Upton, James
- Subjects
- *
LIE groups , *VALUATION , *LOGICAL prediction , *P-adic analysis - Abstract
In this paper we consider a tower of number fields ⋯ ⊇ K (1) ⊇ K (0) ⊇ K arising naturally from a continuous p -adic representation of Gal (Q ¯ / K) , referred to as a p -adic Lie tower over K. A recent conjecture of Daqing Wan hypothesizes, for certain p -adic Lie towers of curves over F p , a stable (polynomial) growth formula for the genus. Here we prove the analogous result in characteristic zero, namely: the p -adic valuation of the discriminant of the extension K (i) / K is given by a polynomial in i , p i for i sufficiently large. This generalizes a previously known result on discriminant-growth in Z p -towers of local fields of characteristic zero. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
29. Complex and tropical counts via positive characteristic.
- Author
-
Pacini, Marco and Testa, Damiano
- Abstract
We study two classical families of enumerative problems: inflection lines of plane curves and theta-hyperplanes of canonical curves. In these problems the complex counts and the tropical counts disagree. Each problem suggests a prime with special behavior. On the one hand, we analyze the reduction modulo these special primes, and we prove that the complex solutions coalesce in uniform clusters. On the other hand, we observe that the counts in special characteristic and in tropical geometry match. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
30. INHERENT FEATURES OF FRACTAL SETS AND KEY ATTRIBUTES OF FRACTAL MODELS.
- Author
-
BALANKIN, ALEXANDER S., ORTIZ, JULIÁN PATIÑO, and ORTIZ, MIGUEL PATIÑO
- Subjects
- *
FRACTALS , *DEGREES of freedom , *ANISOTROPY , *FRACTAL analysis - Abstract
The main goal of this work is to develop a robust framework for an exhaustive description of essential properties of a fractal object. For this purpose, the inherent features of fractal sets are scrutinized. The topological, metrological, morphological, and topographical attributes of fractal systems are delineated. The criteria of the fractal connectedness are established. The characteristics of the fractal connectivity and ramification are ascertained. The index of the fractal loopiness is introduced. The quantifications of the fractal heterogeneity, lacunarity, and anisotropy are briefly sketched out. A set of key attributes which enable a proper characterization of fractal system are suggested. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
31. The construction of modular invariants.
- Author
-
Yang, Chen
- Subjects
- *
MODULAR construction , *FINITE groups , *POLYNOMIAL rings , *MODULAR groups - Abstract
We use the k[V]-module generator of the dual module of the polynomial ring k[V] over its subring of invariants of a finite group to construct modular invariants and show that it behaves better than the transfer homomorphism. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
32. How far is an extension of p-adic fields from having a normal integral basis?
- Author
-
Del Corso, Ilaria, Ferri, Fabio, and Lombardo, Davide
- Subjects
- *
INTEGRALS , *RINGS of integers , *FINITE, The , *FREE groups , *P-adic analysis - Abstract
Let L / K be a finite Galois extension of p -adic fields with group G. It is well-known that O L contains a free O K [ G ] -submodule of finite index. We study the minimal index of such a free submodule, and determine it exactly in several cases, including for any cyclic extension of degree p of p -adic fields. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
33. Cubic function fields with prescribed ramification.
- Author
-
Karemaker, Valentijn, Marques, Sophie, and Sijsling, Jeroen
- Subjects
- *
ELLIPTIC curves , *EQUATIONS - Abstract
This paper describes cubic function fields L / K with prescribed ramification, where K is a rational function field. We give general equations for such extensions, an explicit procedure to obtain a defining equation when the purely cubic closure K ′ / K of L / K is of genus zero, and a description of the twists of L / K up to isomorphism over K. For cubic function fields of genus at most one, we also describe the twists and isomorphism classes obtained when one allows Möbius transformations on K. The paper concludes by studying the more general case of covers of elliptic and hyperelliptic curves that are ramified above exactly one point. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
34. On Huisman's conjectures about unramified real curves.
- Author
-
Kummer, Mario and Manevich, Dimitri
- Subjects
- *
LOGICAL prediction , *ALGEBRAIC curves - Abstract
Let X ⊂ ℙn be an unramified real curve with X(ℝ) ≠ 0. If n ≥ 3 is odd, Huisman [9] conjectured that X is an M-curve and that every branch of X(ℝ) is a pseudo-line. If n ≥ 4 is even, he conjectures that X is a rational normal curve or a twisted form of such a curve. Recently, a family of unramified M-curves in ℙ3 providing counterexamples to the first conjecture was constructed in [11]. In this note we construct another family of counterexamples that are not even M-curves. We remark that the second conjecture follows for generic curves of odd degree from the de Jonquières formula. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
35. AFRICAN TOURISM IN UNCERTAIN TIMES: COVID-19 RESEARCH PROGRESS.
- Author
-
ROGERSON, Christian M. and ROGERSON, Jayne M.
- Subjects
COVID-19 ,DEVELOPING countries ,TOURISM ,TOURISM research - Abstract
COVID-19 is a trigger event which is changing the complexion of African tourism and the directions of African tourism research. This article offers an overview and commentary on the state of African research produced during the uncertain times of 2020-2021 in specific response to the immediate impacts and changes which have been catalysed by the pandemic. The article is a progress report to capture and profile the body of focussed contributions on COVID-19 and tourism which have appeared for sub-Saharan Africa. Further, it is a contribution towards strengthening our understanding of tourism and change in the Global South. Overall, the discussion serves to highlight an emerging African scholarship which is engaged on a range of issues around three core themes of ramification, adaptation and transformation. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
36. RAMIFICATION IN QUARTIC CYCLIC NUMBER FIELDS K GENERATED BY x4 + px² + p.
- Author
-
PÉREZ-HERNÁNDEZ, JULIO and PINEDA-RUELAS, MARIO
- Subjects
QUARTIC fields ,FACTORIZATION ,INTEGRALS ,MATHEMATICAL formulas ,MATHEMATICAL analysis - Abstract
If K is the splitting field of the polynomial f(x) = x
4 + px² + p and p is a rational prime of the form 4+n², we give appropriate generators of K to obtain the explicit factorization of the ideal qOK, where q is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals. [ABSTRACT FROM AUTHOR]- Published
- 2021
- Full Text
- View/download PDF
37. Abhyankar's affine arithmetic conjecture for the symmetric and alternating groups.
- Author
-
Entin, Alexei and Pirani, Noam
- Subjects
- *
FINITE groups , *FINITE fields , *ARITHMETIC , *LOGICAL prediction , *GALOIS theory - Abstract
We prove that for any prime p > 2 , q = p ν a power of p , n ≥ p and G = S n or G = A n (symmetric or alternating group), there exists a Galois extension K / F q (T) ramified only over ∞ with Gal (K / F q (T)) = G. This confirms a conjecture of Abhyankar for the case of symmetric and alternating groups over finite fields of odd characteristic. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
38. On a Local-Global Principle for H 3 of Function Fields of Surfaces over a Finite Field
- Author
-
Pirutka, Alena, Chambert-Loir, Antoine, Series editor, Lu, Jiang-Hua, Series editor, Tschinkel, Yuri, Series editor, Auel, Asher, editor, Hassett, Brendan, editor, Várilly-Alvarado, Anthony, editor, and Viray, Bianca, editor
- Published
- 2017
- Full Text
- View/download PDF
39. ON THE INDICES IN NUMBER FIELDS AND THEIR COMPUTATION FOR SMALL DEGREES.
- Author
-
Bayad, Abdelmejid and Seddik, Mohammed
- Subjects
- *
INDEX numbers (Economics) , *DEDEKIND sums , *FINITE fields , *INTEGERS - Abstract
Let K be a number field. We investigate the indices I(K) and i(K) of K introduced respectively by Dedekind and Gunji-McQuillan. Let n be a positif integer, we then prove that for any prime p < n, there exists K a number field of degree n over Q such that p divide i(K). This result is an analogue to Bauer's one for i(K). We compute I(K) and i(K) for cubic fields and infinite families of simplest number fields of degree less than 7. We solve questions and disprove the conjecture stated in [1 ]. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
40. ON DECOMPOSITION OF A RATIONAL PRIME IN A CUBIC FIELD.
- Author
-
BARAI, RAKESH
- Subjects
INTEGERS ,ALGEBRAIC number theory ,HYPOTHESIS ,NEWTON diagrams ,COEFFICIENTS (Statistics) - Abstract
This article gives an expanded proof of the theorem of Llorente and Nart, [10], on the decomposition of a rational prime in a cubic field. We use this theorem to determine the decomposition of a prime p in a cyclic cubic field as well as in a pure cubic field. [ABSTRACT FROM AUTHOR]
- Published
- 2021
41. A Study on the Anatomical Properties of Arteria Celiaca and Its Branches in Hasak Sheep.
- Author
-
ÖZDEMİR, Derviş, BALKAYA, Hülya, and ÖZÜDOĞRU, Zekeriya
- Subjects
SHEEP ,AORTA ,ARTERIES ,LATEX ,MANDIBULAR ramus - Abstract
Copyright of Firat Universitesi Saglik Bilimleri Veteriner Dergisi is the property of Firat Universitesiu, Saglik Bilimleri Enstitusu and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2021
42. Surveillance and privacy: A ramification of article 21.
- Author
-
Kaur, Rupinder
- Published
- 2018
43. Functional and Metabolic Characterization of Microglia Culture in a Defined Medium
- Author
-
Alejandro Montilla, Alazne Zabala, Carlos Matute, and María Domercq
- Subjects
microglia ,culture ,ramification ,phagocytosis ,metabolic reprogramming ,purinergic receptors ,Neurosciences. Biological psychiatry. Neuropsychiatry ,RC321-571 - Abstract
Microglia are the endogenous immune cells of the brain and act as sensor of infection and pathologic injury to the brain, leading to a rapid plastic process of activation that culminates in the endocytosis and phagocytosis of damaged tissue. Microglia cells are the most plastic cells in the brain. Microglia isolation from their environment as well as culturing them in the presence of serum alter their function and lead to a rapid loss of their signature gene expression. Previous studies have identified pivotal factors allowing microglia culture in the absence of serum. Here, we have further characterized the function, expression of markers, metabolic status and response to pro and anti-inflammatory stimulus of microglia isolated by magnetic-activated cell sorting and cultured in a chemically defined medium. We have compared this new method with previous traditional protocols of culturing microglia that use high concentrations of serum.
- Published
- 2020
- Full Text
- View/download PDF
44. RESULTS OF STUDYING HAIRY VETCH (VICIA VILLOSA ROTH) IN MONO- AND BINARY AGROPHYTOCOENOSES AT SPRING PLANTING UNDER THE CONDITIONS OF THE NORTH-EAST OF THE RUSSIAN FEDERATION
- Author
-
T. G. Aleksandrova, O. I. Kovina, T. V. Shelenga, L. Y. Novikova, and M. A. Vishnyakova
- Subjects
vicia villosa ,вика мохнатая ,популяция ,биотип ,агрофитоценоз ,ветвление ,зеленая масса ,белок ,селекция ,hairy vetch ,population ,biotype ,agrophytocoenosis ,ramification ,green matter ,protein ,breeding ,Biotechnology ,TP248.13-248.65 ,Botany ,QK1-989 - Abstract
Hairy vetch (Vicia villosa Roth), like common vetch (V. sativa L.), is one of the most widespread cultivated forage vetches. In Russia, hairy vetch is sown both in spring and winter planting seasons. V. villosa populations may contain spring, semi-spring, semi-winter and winter biotypes. Three hairy vetch varieties (Nezhnostebelnaya, Siverskaya 2 and Ukrainka) were studied in mono- and binary agrophytocoenosis with oat, rape and barley at spring sowing under the conditions of Leningrad Province of the Russian North-West in 2010-2012. Biotype composition of vetch variety populations was determined to identify adaptive biotypes. Some biological and agronomic characters were analysed. Comparative evaluation of hairy vetch variety populations was performed to test the role of agrophytocoenosis (and its phytocomponent) as a possible factor of biotype variability in vetch varieties and their biological and agronomic characters.
- Published
- 2018
- Full Text
- View/download PDF
45. Functional and Metabolic Characterization of Microglia Culture in a Defined Medium.
- Author
-
Montilla, Alejandro, Zabala, Alazne, Matute, Carlos, and Domercq, María
- Subjects
PHAGOCYTOSIS ,MICROGLIA ,CELL culture ,PURINERGIC receptors ,BRAIN injuries ,GENE expression - Abstract
Microglia are the endogenous immune cells of the brain and act as sensor of infection and pathologic injury to the brain, leading to a rapid plastic process of activation that culminates in the endocytosis and phagocytosis of damaged tissue. Microglia cells are the most plastic cells in the brain. Microglia isolation from their environment as well as culturing them in the presence of serum alter their function and lead to a rapid loss of their signature gene expression. Previous studies have identified pivotal factors allowing microglia culture in the absence of serum. Here, we have further characterized the function, expression of markers, metabolic status and response to pro and anti-inflammatory stimulus of microglia isolated by magnetic-activated cell sorting and cultured in a chemically defined medium. We have compared this new method with previous traditional protocols of culturing microglia that use high concentrations of serum. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
46. RAMIFICATION IN DENTAL PRACTICE WITH THE KNOWLEDGE AND AWARENESS IN THE SUBJECT OF TOOTH MORPHOLOGY.
- Author
-
Qamar, Namerah, Naseer, Hira, Nazir, Shakila, and Merchant, Sabih
- Subjects
PRACTICE of dentistry ,TEETH ,MEDICAL personnel ,STUDENT housing ,AWARENESS ,DENTAL education - Abstract
Background: The concept of assessing that, the knowledge and awareness of the subject of tooth morphology among the final year BDS students and house officers is helpful in their clinical practice. Methodology: The study was conducted among the final year BDS students and house officers. Data was collected by a predesigned proforma. The sample size calculated was 310 by keeping proportion 52% and confidence interval 95% and margin of error 5% in open epi. 3.01. Results: Results of the survey and feedback revealed that the technical difficulties had been faced during clinical practice in different fields of dentistry due to the lack of basic knowledge of the subject. Conclusion: Knowledge and awareness of the subject lays the foundation headed for a skillful dentist and an assertive clinician. [ABSTRACT FROM AUTHOR]
- Published
- 2020
47. Spatio-temporal analysis of strawberry architecture: insights into the control of branching and inflorescence complexity
- Author
-
Labadie, Marc, Guy, Karine, Demené, Marie-Noëlle, Caraglio, Yves, Heidsieck, Gaëtan, Gaston, Amelia, Rothan, Christophe, Guédon, Yann, Pradal, Christophe, Denoyes, Béatrice, Labadie, Marc, Guy, Karine, Demené, Marie-Noëlle, Caraglio, Yves, Heidsieck, Gaëtan, Gaston, Amelia, Rothan, Christophe, Guédon, Yann, Pradal, Christophe, and Denoyes, Béatrice
- Abstract
Plant architecture plays a major role in flowering and therefore in crop yield. Attempts to visualize and analyse strawberry plant architecture have been few to date. Here, we developed open-source software combining two- and three-dimensional representations of plant development over time along with statistical methods to explore the variability in spatio-temporal development of plant architecture in cultivated strawberry. We applied this software to six seasonal strawberry varieties whose plants were exhaustively described monthly at the node scale. Results showed that the architectural pattern of the strawberry plant is characterized by a decrease of the module complexity between the zeroth-order module (primary crown) and higher-order modules (lateral branch crowns and extension crowns). Furthermore, for each variety, we could identify traits with a central role in determining yield, such as date of appearance and number of branches. By modeling the spatial organization of axillary meristem fate on the zeroth-order module using a hidden hybrid Markov/semi-Markov mathematical model, we further identified three zones with different probabilities of production of branch crowns, dormant buds, or stolons. This open-source software will be of value to the scientific community and breeders in studying the influence of environmental and genetic cues on strawberry architecture and yield.
- Published
- 2023
48. Modified defect relation of Gauss maps on annular ends of minimal surfaces for hypersurfaces of projective varieties in subgeneral position.
- Author
-
Quang, Si Duc
- Published
- 2024
- Full Text
- View/download PDF
49. Dual amplification–based ultrasensitive and highly selective colorimetric detection of miRNA.
- Author
-
Asa, Tasnima Alam, Kumar, Pradeep, and Seo, Young Jun
- Subjects
- *
MICRORNA , *CIRCULAR DNA , *PINK , *DETECTION limit , *UBIQUITIN ligases - Abstract
In this study, we combined a Pradeep Kumar (PK)-probe with a ligation–transcription–ramified RCA (LTR) dual-amplification system for the isothermal colorimetric detection of miRNA 25-3P, where the PK-probe transformed from its pink color to colorless in the presence of the amplification byproduct pyrophosphate (PPi), thereby allowing the simple naked-eye qualitative detection of the miRNA. Through this double-amplification strategy, the limit of detection reached as low as 91.4 aM—quite extraordinary sensitivity for a colorimetric miRNA detection system based on absorbance readings. Our detection system also operated with high specificity, the result of using two different target-selective ligation steps (linear DNA ligation and circular DNA ligation) mediated by SplintR ligase, and so could discriminate single-mismatched from perfectly matched target sequences. We suspect that this ultrasensitive and selective PK-probe/LTR dual-amplification system should be a great colorimetric diagnostic for the detection of any miRNA with high efficiency. [Display omitted] • Ultrasensitive (aM scale) colorimetric detection of miRNA managed by Dual-amplification system under isothermal condition. • High selectivity (selective to single mismatch) ensured by two different target-selective twice ligation. • PK-probe/LTR dual-amplification system should be a great colorimetric diagnostic for the detection of any miRNA. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
50. Ramified structure
- Author
-
Uzquiano, Gabriel
- Published
- 2022
- Full Text
- View/download PDF
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