Conjectural Research Articles

On Some Conjectural Supercongruences for Sums Involving Certain Rising Factorials

On Some Conjectural Supercongruences for Sums Involving Certain Rising Factorials

Iranian Urology Association Coronavirus Disease 2019 (COVID-19) Taskforce Pamphlet (IUA-CTP) Recommended Practice based on National Epidemiologic Analysis.

Since the emergence of Covid19 epidemics different guidelines and protocols have been published by Urology associations. Most of these recommendations have focused on the aptitude of any disease or condition for postponement. With the evolution of the outbreak, it is clear that postponement of procedures is not the policy we can rely on exclusively. We must know where do we stand? Where are we going in our country? How useful our recommendations have been for urology practitioners? We try to draw a clearer although-to some extent- conjectural picture and to adjust our protocols to this picture of outbreak evolution. Assuming that anything in this predicament is subject to unexpected changes. For these goals, we raise these arguments in three sections. First, where do we stand and where are we going? Explaining the present situation and best available statistics of the disease, the velocity the disease is spreading and our approximate predicted date its subsidence or partial remission. In a web form survey, we tried to evaluate that in the absence of a clear picture of outbreak progress in a specific area, how useful experts' points of view will be for the urologists working in non-referral centers especially in relevance to equivocal and challenging cases. Will there be any significant difference at all? In the third section, we try to give the plot to guide scheduling or postponing procedures in any given are according to the level of involvement. Here we considered both the characteristics of the special urology condition and also the situation and progress of the outbreak in that area.

On two conjectural supercongruences of Z.-W. Sun

In this paper, we mainly prove two conjectural supercongruences of Sun by using the following identity: $$\begin{aligned} \sum _{k=0}^n\left( {\begin{array}{c}2k k\end{array}}\right) ^2\left( {\begin{array}{c}2n-2k n-k\end{array}}\right) ^2=16^n\sum _{k=0}^n \frac{\left( {\begin{array}{c}n+k k\end{array}}\right) \left( {\begin{array}{c}n k\end{array}}\right) \left( {\begin{array}{c}2k k\end{array}}\right) ^2}{(-16)^k}, \end{aligned}$$ which arises from a $${}_4F_3$$ hypergeometric transformation. For any prime $$p>3$$ , we prove that $$\begin{aligned}&\sum _{n=0}^{p-1}\frac{n+1}{8^n}\sum _{k=0}^n\left( {\begin{array}{c}2k k\end{array}}\right) ^2 \left( {\begin{array}{c}2n-2k n-k\end{array}}\right) ^2\equiv (-1)^{(p-1)/2}p+5p^3E_{p-3}\pmod {p^4},\\&\sum _{n=0}^{p-1}\frac{2n+1}{(-16)^n} \sum _{k=0}^n\left( {\begin{array}{c}2k k\end{array}}\right) ^2\left( {\begin{array}{c}2n-2k n-k\end{array}}\right) ^2\equiv (-1)^{(p-1)/2}p +3p^3E_{p-3}\pmod {p^4}, \end{aligned}$$ where $$E_{p-3}$$ is the $$(p-3)\hbox {th}$$ Euler number.

Two q-congruences from Carlitz’s formula

Recently, using a formula of Carlitz, the second author proved a q-congruence conjectured by Tauraso. In this note we utilize Carlitz’s formula to prove two more similar q-congruences. We also propose a conjectural q-congruence that refines one of our q-congruences.

Fou Yusuf V ibn Ahmad, rei de Granada, l'infant Coix de les cròniques castellanes?

L'historiographie avait identifié, traditionnellement, l'infant Cojo de Grenade qui apparait aux chroniques castillanes avec Muhammad X ibn Utman, alors qu'avait assimilé Yusuf ibn Ahmad avec l'Aben Ismael des chroniques. La thèse de M. Charouiti, qui édite et étudie une oeuvre du grenadin Ibn Asim, contemporain aux événements, que l'on considérait perdue, démontre que Yusuf et Ismail furent deux personnes différentes. Alors, une revision des données que cet ouvrage nous apporte, de quelques nouvelles données inédites des archives catalans et de la présence de l’infant Cojo aux chroniques castillanes, lesquelles ne l'appellent jamais Muhammad, nous permet découvrir que Yusuf V ibn Ahmad pourrait être l'infant Cojo des chroniques, et que la supposition de l'existence de ce Muhammad X el Cojo avait été produite par l'homonymie des sultans grenadins du XVe. siècle, par les imprécisions en leur succession et par les erreurs, avec une longue tradition, dans l'attribution de leurs appellatifs.

On some conjectural hypergeometric congruences

In this paper, we confirm some congruences conjectured by V.J.W. Guo and M.J. Schlosser recently. For example, we show that for primes $p>3$, $$ \sum_{k=0}^{p-1}(2pk-2k-1)\frac{\left(\frac{-1}{p-1}\right)_k^{2p-2}}{(k!)^{2p-2}}\equiv0\pmod{p^5}. $$

Supercongruences for sums involving rising factorial

ABSTRACTFor integers and , denote by and the sums given by and respectively. In this paper, we deduce certain supercongruence relations for and . As particular cases, we give proofs of some conjectural supercongruences of Guo.

CONGRUENCES FOR THE TH APÉRY NUMBER

We prove two conjectural congruences on the $(p-1)$ th Apéry number, which were recently proposed by Z.-H. Sun.

A Case of Prolonged Erection Treated with Subcutaneous Terbutaline

Prolonged erection is a relatively uncommon phenomenon and can become a medical emergency if it progresses to priapism. Even though appropriate management of priapism and prolonged erection supports early involvement of urologists, this may not always be feasible due to unavailability of these specialists. In such scenarios, conservative non-surgical methods must be attempted. However, very few guidelines and evidence-based treatment modalities exist in the literature making management of prolonged erection conjectural and challenging. Here we describe a case of prolonged erection successfully resolved with subcutaneous terbutaline.

Congruence Primes of the Kim–Ramakrishnan–Shahidi Lift

ABSTRACTFor a primitive form f of weight k for let KS(f) be the Kim–Ramakrishnan–Shahidi (K–R–S) lift of f to the space of cusp forms of weight for Based on some working hypothesis, we propose a conjecture, which relates the ratio of the periods (Petersson norms) to the symmetric 6th L-value L(3k − 2, f, Sym6) of f. From this, we also propose that a prime ideal dividing the (conjectural) algebraic part L(3k − 2, f, Sym6) of L(3k − 2, f, Sym6) gives a congruence between the K–R–S lift and non-K–R–S lift, and test this conjecture numerically.

The New Cambridge Companion to Shakespeare

Preface William Shakespeare: a partial chronology Shakespeare's works: a conjectural chronology 1. The traces of Shakespeare's life STEPHEN GREENBLATT 2. Shakespeare's reading JEFF DOLVEN and SEAN KEILEN 3. Shakespeare's writing H. R. WOUDHUYSEN 4. The theatre of Shakespeare's London TIFFANY STERN 5. Transmission of Shakespeare's texts ANDREW MURPHY 6. Shakespeare and language JONATHAN HOPE 7. Shakespeare the poet COLIN BURROW 8. Shakespeare's comedies STANLEY WELLS 9. Shakespeare's tragedies MICHAEL NEILL 10. Shakespeare's English history plays TON HOENSELAARS 11. Shakespeare's Classical plays HEATHER JAMES 12. Shakespeare's tragicomedies JANETTE DILLON 13. Shakespeare, religion and politics CLAIRE MCEACHERN 14. Shakespeare and race JONATHAN GIL HARRIS 15. Shakespeare, sex and gender STEPHEN ORGEL 16. Shakespeare's stage ANTHONY DAWSON 17. The critical reception of Shakespeare EMMA SMITH 18. Shakespeare and popular culture PAUL PRESCOTT 19. Shakespeare and globalization ANSTON BOSMAN 20. Shakespeare and media history KATHERINE ROWE 21. Shakespeare: reading on ANDREW DICKSON.

A Conjectural Study

A Conjectural Study

Spatial planning, legislation and the historical and contemporary challenges in Zimbabwe: A conjectural approach

This paper seeks to unravel the spatial planning system in Zimbabwe in cognisance of its potential role to addressing some of the skewed phenomena of planning in the country. Some of the contemporary planning challenges are rooted in the colonial footprints, emanating from the Rhodesian segregationist policies and repressive legislation that have continued to exist into the ‘free Zimbabwean’ era despite having outlived their relevance and usefulness, to modern day Zimbabwe. The situation is not peculiar to Zimbabwe alone but it cuts through many African counties. Key words: Spatiality, planning, legislation, colonialism, post-coloniality, poverty, policy

The conjectural body: gender, race, and the philosophy of music

The conjectural body: gender, race, and the philosophy of music

Beyond What Is Written: Erasmus and Beza as Conjectural Critics of the New Testament

Beyond What Is Written: Erasmus and Beza as Conjectural Critics of the New Testament

Beyond What Is Written: Erasmus and Beza as Conjectural Critics of the New Testament

Beyond What Is Written: Erasmus and Beza as Conjectural Critics of the New Testament

A Study of conjectural expressions in Japanese: ー Focusing on the comparison of rashii and youda -

A Study of conjectural expressions in Japanese: ー Focusing on the comparison of rashii and youda -

Beyond What is Written: Erasmus and Beza as Conjectural Critics of the New Testament – By Jan Krans

Beyond What is Written: Erasmus and Beza as Conjectural Critics of the New Testament – By Jan Krans

Representational vs conjectural divination: innovating out of nothing in Mongolia

Divination is often regarded as a practice undertaken to obtain a standardized, best possible result. This characterization is made at the cost of analysing how people obtain desired innovations through divinatory procedures. To show how divination actually forces people to adopt strategies that lead to innovation, this article classifies all forms of divination into ‘representational’ or ‘conjectural’ categories. Drawing on Mongolian ethnography, the article argues that in conjectural divinations repeated questioning links known impossibilities to prospective possibilities, producing the basis for innovations which initially appear to arise out of nothing. The article demonstrates how conjectural divinations initiate processes of innovation wherein repeated questioning leads to combinatory thought which imposes novel combinations on people, who perceive the need for innovation, access an innovation, and finally recursively posit that innovation’s conceptual origins.

Le prix de la fixité : Application à l'Union monétaire des Caraïbes orientales et à la Zone franc

Les gouvernements aliènent l’arme du change pour bénéficier d’une politique monétaire plus crédible de manière à stabiliser leur monnaie. Cette politique a un coût car il y a un risque d’appréciation réelle du taux de change. Les solutions de coin fixes que nous appelons "union de taux de change" (Bordo, Jonung 1999) suppriment un grand nombre des causes de l’appréciation. En revanche, lorsqu’une déviation du taux de change réel vis-à-vis de son niveau d’équilibre survient, elles recourent à un ajustement passif ou automatique fondé sur la déflation. Le coût conjoncturel des pressions déflationnistes dépend de la présence des rigidités nominales qui sont, elles, influencées par la taille des économies. Les pays de la Zone franc s’affranchissent des contraintes de la fixité grâce à leur possibilité de financement en devises auprès du compte d’opérations. Ainsi, ils évitent le coût conjoncturel des déviations ponctuelles du change réel, mais restent soumis à l’inertie des chocs inflationnistes suscités par les autorités.