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a.va.ces in Pure Ma.hema.ics 2024年第5期14卷 321-332页

作者： Ma.y ndiaye Middle School Ba.a.a.Mba.e Ka.a Dakar Academy Inspection Ministry of National Education of Senegal Dakar Senegal

We ha.e found through ca.cula.ions tha. the differences between the closest supposed prime numbers other tha. 2 a.d 3 defined in the a.ticles a.e: 2;4: a.d 6. For those whose difference is equa. to 6, we showed their origin then we cla.sified them into two ca.egories a.cording to their cla.ses, we showed in which context two prime numbers which differ from 6 a.e ca.led sexy a.d in wha. context they a.e sa.d rea. sexy prime. For those whose difference is equa. to 4, we showed their origin then we showed tha. two prime numbers which differ from 4, tha. is to sa. two cousin prime numbers, a.e successive. We ma.e a. observa.ion on the supposed prime numbers then we esta.lished two pa.rs of equa.ions from this observa.ion a.d deduced the origin of the Mersenne number a.d tha. of the Ferma. number.

关键词： Cousin Prime Numbers Sexy Prime Numbers Rea. Sexy Prime Numbers Equa.ions from Supposed Prime Numbers Mersenne Number Ferma. Number Supposed Prime Numbers Prime Numbers

Ma.rix Ricca.i Equa.ions in Optima. Control

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a.plied Ma.hema.ics 2024年第3期15卷 199-213页

作者： Ma.ick ndiaye School of Computer Sciences a.d Ma.hema.ics Marist College Poughkeepsie USA

In this pa.er, the ma.rix Ricca.i equa.ion is considered. There is no genera. wa. for solving the ma.rix Ricca.i equa.ion despite the ma.y fields to which it a.plies. While sca.a. Ricca.i equa.ion ha. been studied thoroughly, ma.rix Ricca.i equa.ion of which sca.a. Ricca.i equa.ions is a.pa.ticula. ca.e, is much less investiga.ed. This a.ticle proposes a.cha.ge of va.ia.le tha. a.lows to find explicit solution of the Ma.rix Ricca.i equa.ion. We then a.ply this solution to Optima. Control.

关键词： Optima. Control Ma.rix Ricca.i Equa.ion Cha.ge of Va.ia.le

Prelimina.y Identifica.ion of a.Prime Number Other Tha. 2 a.d 3, the Origin of Twin Prime Numbers, the Structure of the Cha.n of Prime Numbers a.d the Set of Prime Numbers Less Tha. a.Given Integer

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a.va.ces in Pure Ma.hema.ics 2024年第1期14卷 30-48页

作者： Ma.y ndiaye Middle School Ba.a.a.Mba.e Ka.a.Da.a. a.a.emy Inspection Ministry of National Education of Senegal Dakar Senegal

The a.plica.ion of the Euclidea. division theorem for the positive integers a.lowed us to esta.lish a.set which conta.ns a.l the prime numbers a.d this set we ca.led it set of supposedly prime numbers a.d we noted it Esp. We subsequently esta.lished from the previous set the set of non-prime numbers (the set of numbers belonging to this set a.d which a.e not prime) denoted Enp. We then extra.ted from the set of supposedly prime numbers the numbers which a.e not prime a.d the set of rema.ning number constitutes the set of prime numbers denoted Ep. We ha.e deduced from the previous set, the set of prime numbers between two na.ura. numbers. We ha.e expla.ned during our demonstra.ions the origin of the twin prime numbers a.d the structure of the cha.n of prime numbers.

关键词： Supposedly Prime Numbers Non-Prime Numbers Prime Numbers Prime Numbers Less Tha. a.Given Integer Prime Numbers between Two Given Integers

Sinona.a. Polyposis: a.out 60 Ca.es a. Fa.n University Hospita. Center, Senega.

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Interna.iona. Journa. of Otola.yngology a.d Hea. & Neck Surgery 2024年第1期13卷 53-61页

作者： Ma.e Sa.ou Diouf Mousta.ha.ndiaye a.ma.ou Dembele Evelyne Siga.Diom Ciré ndiaye a.a.ou Thia. Richa.d E. a. Deguenonvo a.dou Sy Ma.ick ndiaye a.doura.ma.e Ta.l Issa.Cheikh ndiaye Ra.mond Diouf HOGIP Hospita. Center Dakar Senegal Fa.n University Hospita. Center Dakar Senegal Ourossogui Hospita. Center Matam Senegal La.Pa.x Hospita. Center Ziguinchor Senegal Children Hospita. Center of Dia.nia.io Dakar Senegal

Introduction: Sinona.a. polyposis (SNP) is a.chronic infla.ma.ory disea.e of the mucosa.of the na.a. ca.ities a.d fa.ia. sinuses. It is cha.a.terized by a. oedema.ous, multifoca. a.d bila.era. degenera.ion of the na.osinus mucosa. which origina.es in the la.era. ma.ses of the ethmoid, where it ca.ses the forma.ion of smooth, gela.inous, tra.slucent a.d pyriform polyp lesions. The objective of this study wa. to review epidemiologica., clinica., pa.a.linica. da.a.a.d eva.ua.e the results of endoscopic surgica. trea.ment. Pa.ients a.d Methods: This is a.retrospective study on 60 pa.ients followed a. the ENT depa.tment of the Fa.n Na.iona. University Hospita. Center, from Ja.ua.y 2010 to December 2015. a.l pa.ients with sinona.a. polyposis were included in the study. Results: The a.era.e a.e of our pa.ients wa. 38 yea.s a.d the sex ra.io (M/F) wa. 0.8. In the pa.ients’ histories, we found 18% a.thma.a.d 10% Wida.’s disea.e. The a.era.e consulta.ion time wa. 8.5 yea.s. a.l pa.ients ha. consulted for na.a. obstruction;rhinorrhea.wa. bila.era. a.d found in 67.7% of ca.es, with olfa.tory disorders a.counting for 50%. The CT sca. performed in 58% of ca.es ma.e it possible to specify the extent of the lesions;the involvement of the ethmoida. sinus wa. consta.t a.d extended to the other sinuses except in 2 ca.es. a.l pa.ients ha. received medica. trea.ment with loca. corticosteroids. Endoscopic surgica. trea.ment wa. initia.ed in 43% of ca.es a.ter fa.lure of corticosteroid-ba.ed medica. trea.ment. The evolution under trea.ment ma.ked by the rea.pea.a.ce of symptoms tha. increa.ed ea.h month. a. one month postopera.ively, a.l clinica. symptoma.ology ha. improved with the exception of olfa.tory disorders, which persisted in 3 pa.ients. a. 12 months we noted 12 ca.es of rea.pea.a.ce of na.a. obstruction. Conclusion: SNP is a.disea.e of little known etiology. The dia.nosis is a.most a.wa.s clinica.. Endoscopic surgery rema.ns a.recourse to medica. trea.ment. For good loca. contro

关键词： Sinona.a. Polyposis Endona.a. Endoscopic Surgery CHNU Fa.n

Hydrologica. Modelling of the Ca.a.a.ce River in Its Upstrea. Section (Ba.in a. Kolda.Level) to Predict Its Future Sta.es a. a.Function of Different Stresses

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Open Journa. of Geology 2024年第2期14卷 143-154页

作者： Coumba.ndiaye Sa.dou Nda. La.ora.ory of Wa.er a.d Environment Sciences a.d Technologies (La.TEE) Polytechnic School of Thies (EPT) Thies Senegal UFR Sciences a.d Technologies (SET) University Iba Der Thiam of Thies (UIDT) Thies Senegal

Flow records for sta.ions in the Ca.a.a.ce ba.in a.e incomplete. Severa. ga.s were noted over the 1980-2021 study period, ma.ing this study tedious. The a.m of this study is to a.sess the potentia. impa.t of clima.e cha.ge on the flow of the Ca.a.a.ce wa.ershed a. Kolda. To this end, hydrologica. series a.e simula.ed a.d then extended using the GR2M ra.nfa.l-runoff model, with a.monthly time step. Projected clima.e da.a.a.e derived from a.multi-model ensemble under scena.ios SSP2-4.5 (scena.io with a.ditiona. ra.ia.ive forcing of 4.5 W/m2 by 2099) a.d SSP5-8.5 (scena.io with a.ditiona. ra.ia.ive forcing of 8.5 W/m2 by 2099). a. a.a.ysis of the homogeneity of the ra.nfa.l da.a.series from the Kolda.sta.ion wa. ca.ried out using KhronoSta. softwa.e. The Ca.a.a.ce wa.ershed wa. then delimited using a.cGIS to determine the morphometric pa.a.eters of the ba.in, which will be decisive for the rest of the work. Next, monthly eva.otra.spira.ion wa. ca.cula.ed using the formula.proposed by Oudin et a.. This, together with ra.nfa.l a.d runoff, forms the input da.a.for the model. The GR2M model wa. then ca.ibra.ed a.d cross-va.ida.ed using va.ious simula.ions to a.sess its performa.ce a.d robustness in the Ca.a.a.ce wa.ershed. The version of the model with the ca.ibra.ed pa.a.eters will ma.e it possible to extend Ca.a.a.ce river flows to 2099. This simula.ion of future flows with GR2M shows a.decrea.e in the flow of the Ca.a.a.ce a. Kolda.with the two scena.ios SSP2-4.5 a.d SSP5-8.5 during the ra.ny period, a.d a.most zero flows during the dry sea.on from the period 2040-2059.

关键词： Ca.a.a.ce Wa.ershed Clima.e Cha.ge GR2M Clima.e Models

Obstructive Tumor of the Pa.a.e in the Old Person: a.Ca.e Report

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Open Journa. of Stoma.ology 2024年第5期14卷 199-205页

作者： Silly Toure Mouha.a.ou Ma.hta. ndiaye a.ibou ndiaye Ma.a.ou Coume Ma.e Sa.ou Diouf Ba.e Ka.im Dia.lo Ma.illofa.ia. Surgery a.d Stoma.ology Depa.tment Aristide Le Dantec University Hospital of Dakar Dakar Senegal Geria.rics Depa.tment Aristide Le Dantec University Hospital of Dakar Dakar Senegal ENT a.d Hea. a.d Neck Surgery Depa.tment FANN University Hospital of Dakar Dakar Senegal

Introduction: Pleomorphic a.enoma.or mixed sa.iva.y gla.d tumor is a.heterogeneous benign tumor of the sa.iva.y gla.ds. The most common site is the pa.otid gla.d. Its extra.pa.otid loca.ions, pa.ticula.ly in the a.cessory sa.iva.y gla.ds, a.e ra.er. We report a.ca.e of a.pleomorphic a.enoma.of the posterior pa.a.e which posed ma.a.ement problems. Observa.ion: This is a. 85-yea.-old pa.ient who consulted for a.tumor of the posterior pa.a.e tha. ha. been evolving for 3 yea.s. The exa.ina.ion revea.ed a.globula. tumor of the posterior pa.a.e extending beyond the midline by a.proxima.ely 7 cm in long a.is, shooting towa.ds the oropha.ynx a.d hindering brea.hing, speech a.d ea.ing, indica.ing a.life-sa.ing tra.heotomy. a.CT sca. of the fa.ia. a.ea.revea.ed a.well-circumscribed tumor a. the expense of the soft pa.a.e, with multiple sites of bone lysis. The biopsy performed wa. in fa.or of a.pleomorphic a.enoma. The pa.ient underwent tota. surgica. excision of a.huge tumor on the pa.a.e. The a.terma.h of the opera.ion wa. ma.ked by a.loosening of the sutures with a. orona.a. fistula.requiring the crea.ion of a. obtura.or pla.e due to the pa.ient’s refusa. to ha.e a.other opera.ion. Conclusion: La.ge pleomorphic a.enoma.of the posterior pa.a.e is a.ra.e entity tha. ca. ca.se respira.ory problems a.d surgica. difficulties. His prognosis is genera.ly good.

关键词： Pleomorphic a.enoma Posterior Pa.a.e Respira.ory Disorders Prognosis Obtura.or Pla.ue

Cha.a.teriza.ion of Wa.tewa.er in School Environments for a. Ecologica. Trea.ment Solution: a.Ca.e Study of Ndiebene Ga.diol 1 School

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Journa. of Wa.er Resource a.d Protection 2024年第1期16卷 27-40页

作者： Fa.ilou Coundoul a.dou Kha.or ndiaye a.doula.e Deme Polytechnic Institute of Sa.nt-Louis Gaston Berger University Saint-Louis Sénégal a.plied Sciences a.d Technologies Tra.ning a.d Resea.ch Unit Gaston Berger University Saint-Louis Sénégal

The study conducted a. Ndiebene Ga.diol 1 school in Senega. ha. unveiled serious environmenta. a.d public hea.th cha.lenges. The wa.tewa.er a.a.ysis revea.ed high levels of Biochemica. Oxygen Dema.d (BOD5), Chemica. Oxygen Dema.d (COD), a.d feca. coliforms, signa.ing potentia. risks to the well-being of students a.d sta.f. This situa.ion mirrors a.wider issue in rura. educa.iona. settings, where ina.equa.e sa.ita.ion persists. Intensive wa.tewa.er trea.ment options a.e known for their effectiveness a.a.nst high polluta.t loa.s but a.e resource-intensive in both energy a.d cost. Conversely, extensive trea.ment systems, while requiring more la.d, provide a.susta.na.le a.terna.ive by ha.nessing na.ura. processes for polluta.t remova.. The resea.ch suggests a.hybrid trea.ment a.proa.h could serve the school’s needs, ba.a.cing the robust ca.a.ilities of intensive methods with the ecologica. benefits of extensive systems. Such a.solution would need to be ta.lored to the specific environmenta., fina.cia., a.d logistica. context of the school, ba.ed on comprehensive fea.ibility studies a.d sta.eholder enga.ement. This study’s findings underscore the urgency of a.dressing sa.ita.ion in schools, a. it is intrinsica.ly linked to the hea.th a.d a.a.emic success of students. Quick, effective, a.d long-term stra.egies a.e vita. to secure a.hea.thier a.d more prosperous future for the youth. With proper implementa.ion, the school ca. tra.sform its sa.ita.ion fa.ilities, setting a.precedent for rura. educa.iona. institutions in Senega. a.d simila. contexts globa.ly.

关键词： Wa.tewa.er Cha.a.teriza.ion Ecologica. Trea.ment School Sa.ita.ion Phytoremedia.ion Rura. Infra.tructure Environmenta. Hea.th

Ma.a.ement of Squa.e Ca.cinoma.of the Lower Lip Using Ca.ille-Berna.d Fla. under Loca. a.esthesia. When Constra.nts Dicta.e Our a.titude

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Open Journa. of Stoma.ology 2024年第4期14卷 191-197页

作者： Silly Toure Mouha.a.ou Ma.hta. ndiaye a.ibou ndiaye Ma.e Sa.ou Diouf Bira.e Loum Ba.e Ka.im Dia.lo Depa.tment of Ma.illofa.ia. Surgery a.d Stoma.ology CHU Aristide Le Dantec of Dakar Dakar Senegal ENT Depa.tment Fann University Hospital Dakar Senegal

Introduction: Squa.ous cell ca.cinoma. of the lip essentia.ly pose a.thera.eutic ma.a.ement problem. In the West, their trea.ment is done under genera. a.esthesia.a.d follows the cla.sic rules of oncology. In our context of exercise, we sometimes ha.e a.different a.titude dicta.ed by va.ious constra.nts. Observa.ion: 55-yea.-old pa.ient with no nota.le history, seen in consulta.ion for a.very la.ge ulcera.ive-budding lesion on the right 2/3 of the lower lip with mucocuta.eous involvement without lymph node findings found on exa.ina.ion. Fa.ed with this suspicious lesion a.d the pa.ient’s fina.cia. difficulties, we decided to opera.e under loca. a.esthesia.to remove this tumor. The oncologica. excision wa. followed by immedia.e pla.ty using a.Ca.ille-Berna.d fla. with a.good immedia.e a.sthetic a.d functiona. result a.d postopera.ive da. 7. The pa.ient wa. una.le to ta.e his surgica. specimen to a.a.omy-pa.hology a.d wa. lost to follow-up due to la.k of fina.cia. resources. On a.a.omo-pa.hologica. a.a.ysis of the surgica. specimen, the ma.gins were hea.thy with confirma.ion of squa.ous cell ca.cinoma.(a.a.a.hologica. rea.ing ma.e for scientific interest). Discussion: The pa.ticula. menta.ity of certa.n pa.ients a.d their difficult fina.cia. conditions push us to ha.e a. unconventiona. thera.eutic a.titude in oncology, but which nevertheless ma.es it possible to resolve certa.n problems tha. we often fa.e. Loca. a.esthesia.is possible a.d rea.istic in ca.es like ours a.d the results ca. be a.cepta.le a.d life-sa.ing.

关键词： Squa.ous Cell Ca.cinoma Lower Lip Ca.ille Berna.d Fla. Loca. a.esthesia

When the Combina.ion of a.Chinese Fla. a.d Dufourmentel Ma.es It Possible to Trea. a.Hopeless Ca.e of Squa.ous Cell Ca.cinoma.of the Upper Lip

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Open Journa. of Stoma.ology 2024年第7期14卷 327-335页

作者： Silly Toure a.ibou ndiaye Mouha.a.ou Ma.hta. ndiaye Ma.a.ou Coume Ma.e Sa.ou Diouf Ba.e Ka.im Dia.lo Depa.tment of Ma.illofa.ia. Surgery a.d Stoma.ology CHU Aristide Le DANTEC Dakar Senegal Geria.rics Depa.tment CHU AT LE DANTEC Dakar Senegal Otorhinola.yngology a.d Hea. a.d Neck Surgery Depa.tment FANN University Hospital Dakar Senegal

Ca.cers of the lip a.e the lea.ing ca.se of la.ia. defects, a.d trea.ment is essentia.ly surgica.. The success of a.repa.r is a.sessed by two essentia. criteria. The functiona. cha.a.ter of the lip (restora.ion of continence a.lowing feeding) a.d the a.sthetic qua.ity of the repa.r. However, for ma.y pa.ients from countries whose medica. infra.tructure does not a.low them to underta.e complex reconstructions loca.ly, medica. tra.sfers represent their only cha.ce of trea.ment. The a.m of this a.ticle is to sha.e with you a. extreme clinica. ca.e of la.ia. reconstruction, the ma.a.ement of which wa. a.rea. cha.lenge, using two ma.or fla.s: the free a.te-bra.hia. fla. a.d the DUFOURMENTEL-type bi-pedicula.ed sca.p fla..

关键词： Surgica. Fla. Reconstruction a.sthetic Lip Ca.cer-Pla.tic Surgery

Ecologica. Wa.tewa.er Trea.ment System Using a.Horizonta. Flow Biologica. Rea.tor: The Ca.e of Vetiver

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Journa. of Environmenta. Protection 2024年第1期15卷 26-38页

作者： Fa.ilou Coundoul a.dou Kha.or ndiaye a.doula.e Deme Polytechnic Institute of Sa.nt-Louis Gaston Berger University Saint-Louis S&eacuten&eacutegal a.plied Sciences a.d Technologies Tra.ning a.d Resea.ch Unit Gaston Berger University Saint-Louis Saint-Louis S&eacuten&eacutegal

Confronted with the cha.lenge of wa.tewa.er ma.a.ement, pa.ticula.ly in the school environment of Senega., our study set out to a.hieve multiple objectives. Following field surveys, la.ora.ory a.a.yses of wa.tewa.er sa.ples were ca.ried out, revea.ing a.significa.t polluta.t loa.. In the community of Ga.diol, nea. Sa.nt-Louis (Senega.), the school of Ndiebene Ga.diol 1 fa.es significa.t sa.ita.ion cha.lenges. Our study a.med to a.dress this issue by using a.constructed filter composed of two filtering bed cells mea.uring 12 × 8.5 m, preceded by a.septic ta.k. We pa.ticula.ly focused on the influence of Vetiver;a.pla.t chosen for its purifica.ion potentia.. Our a.a.yses showed rema.ka.le efficiency of the filter. Elimina.ion ra.es rea.hed 95% for 5-Da. Biochemica. Oxygen Dema.d (BOD5), 91% for Chemica. Oxygen Dema.d (COD), a.d 92% for SS, fa. exceeding the Senega.ese sta.da.ds set a. 50 mg/L, 200 mg/L, a.d 40 mg/L, respectively. Furthermore, the concentra.ion of feca. coliforms wa. reduced to 176 FCU/100mL, well below the Senega.ese threshold of 2000 FCU/100mL a.d close to the World Hea.th Orga.iza.ion’s (WHO) recommenda.ion of 1000 FCU/100mL. However, despite these promising results, some pa.a.eters, pa.ticula.ly the concentra.ion of certa.n polluta.ts, a.proa.hed the thresholds defined by Europea. legisla.ion. For exa.ple, for Suspended Solids (SS), the post-trea.ment level of 3 mg/L wa. well below the Senega.ese sta.da.d but edged close to the Europea. minimum of 10 mg/L. In conclusion, the Vetiver filter demonstra.ed a.rema.ka.le a.ility to trea. school wa.tewa.er, offering high polluta.t elimina.ion percenta.es. These results suggest significa.t opportunities for the reuse of trea.ed wa.er, potentia.ly in a.ea. such a. irriga.ion, though some a.justments ma. be necessa.y to meet the strictest sta.da.ds such a. those of the Europea. union (EU).

关键词： Hydra.lic Engineering Wa.tewa.er Qua.ity Wa.tewa.er Trea.ment a.ricultura. Irriga.ion Sa.ita.ion Engineering Environment