Love for Equa­tions Through­out Life

Uzbekistan Today (English) - - TODAY IN UZBEKISTAN - El­dor Sat­torov

On De­cem­ber 17 in Tashkent, the Repub­li­can sci­en­tific con­fer­ence on “Ac­tual prob­lems of dif­fer­en­tial equa­tions and their ap­pli­ca­tions” will be­gin at the Mirzo Ulug­bek Na­tional Univer­sity of Uzbek­istan. The for­eign sci­en­tists will take part in the event.

Our cor­re­spon­dent met with one of its or­ga­niz­ers, the fa­mous sci­en­tist, Doc­tor of Phys­i­cal and Math­e­mat­i­cal Sciences, Pro­fes­sor Bo­zor Is­lo­mov, and asked him to tell about the goals and tasks of this fo­rum.

- The pur­pose of the sci­en­tific con­fer­ence is to dis­cuss the cur­rent state and prospects for the de­vel­op­ment of the main di­rec­tions of the the­ory of par­tial dif­fer­en­tial equa­tions and math­e­mat­i­cal physics and its ap­pli­ca­tions. The sci­en­tific pro­gram of the con­fer­ence cov­ers such ar­eas as par­tial dif­fer­en­tial equa­tions, math­e­mat­i­cal physics, dy­nam­i­cal sys­tems, func­tion the­ory and func­tional anal­y­sis, math­e­mat­i­cal mod­el­ing, and com­pu­ta­tional meth­ods. - To what ex­tent this fo­rum is rep­re­sen­ta­tive?

- Ev­ery year sci­en­tists of the CIS and other for­eign coun­tries take part in th­ese con­fer­ences held in our repub­lic. This year it will be at­tended by about 50 math­e­ma­ti­cians from Rus­sia, Kaza­khstan, Ta­jik­istan and Kyr­gyzs­tan, as well as more than 140 sci­en­tists from our coun­try.

- What can you say about the con­tri­bu­tion of Uzbek sci­en­tists and math­e­ma­ti­cians to the de­vel­op­ment of this sci­ence?

- To­day, ev­ery ed­u­cated per­son knows the name of Muham­mad al-Khorezmi, im­mor­tal­ized in the term “al­go­rithm”, and founded by him al­ge­bra. Be­fore him, math­e­mat­ics meant ba­si­cally ge­om­e­try with a cer­tain dose of num­ber the­ory.

The work of the sci­en­tist “The Short Book of Re­plen­ish­ment and Con­tra­dic­tion”, along with Eu­clid’s book “The Be­gin­ning” laid the foun­da­tion for the mod­ern math­e­mat­ics. It was rewrit­ten many times in the orig­i­nal lan­guage and trans­lated into Latin, as a re­sult its name be­ing re­duced to the word “al­jabra” “al­ge­bra”.

In his book Al-Khorezmi fo­cused on two op­er­a­tions – “al­jabr” and “al­muk­a­bala”, which, un­like arith­metic, al­low per­form­ing four arith­metic op­er­a­tions on ex­pres­sions con­tain­ing an un­known. That was re­ally a great idea.

This is not co­in­ci­dence, that I did an ex­cur­sion into his­tory. It is as­ton­ish­ing how Muham­mad al-Khorezmi was per­spi­ca­cious when he called of his trea­tise not the con­cept of the equa­tion, namely the ti­tle of a pair of op­er­a­tions! In the fu­ture, more and more new types of al­ge­bras were in­tro­duced. It is pleas­ant to note that one of them - the topo­log­i­cal Boolean al­ge­bras, that was de­vel­oped by Uzbek math­e­ma­ti­cians un­der Aca­demi­cian Tash­muhamed Sarym­sakov in Tashkent. The monograph, writ­ten by him to­gether with his col­leagues, was re­pub­lished in the USA in English trans­la­tion, and then it was awarded the Abu Ray­han Beruni State Prize. And at present this whole di­rec­tion of math­e­mat­ics is in­ten­sively de­vel­op­ing within the frame­work of the sci­en­tific school.

An im­por­tant role in the cog­ni­tion of na­ture plays the sym­me­try prop­erty, which is re­flected in math­e­mat­i­cal models. To ex­press the most gen­eral con­cept of the sym­me­try of geo­met­ric ob­jects, the Nor­we­gian sci­en­tist So­phus Lee in­tro­duced the no­tion of a con­tin­u­ous group. Such ob­jects turned out to be very dif­fi­cult to in­ves­ti­gate ex­ist­ing means at that time. Then the math­e­ma­ti­cians turned to an idea on at­tract­ing a spe­cial al­ge­bra that is quite sim­i­lar to Muham­mad al-Khorezmi’s views. Thus, the no­tion of Lie al­ge­bra ap­peared. Later, other sim­i­lar al­ge­bras were dis­cov­ered, which made it nec­es­sary to study them in the most gen­eral form. At present, this task is be­ing suc­cess­fully de­vel­oped by Uzbek math­e­ma­ti­cians.

- Bo­zor Is­lam­ovich, and how did you come to math­e­mat­ics?

“I was still rav­ing about it at school, I could not fall asleep, if I couldn’t do a sum or an equa­tion. And from the be­gin­ning of the stu­dent’s bench, I joined the re­search work. Af­ter lis­ten­ing to the spe­cial cour­ses of Aca­demi­cian M. Salakhid­di­nov, I be­came in­ter­ested in dif­fer­en­tial equa­tions and equa­tions of math­e­mat­i­cal physics. Since 1979 I have been con­duct­ing sci­en­tific re­search re­lated to the so­lu­tion of bound­ary-value sums of a new type.

In 1981, a new stage of my sci­en­tific ac­tiv­ity in the In­sti­tute of Math­e­mat­ics of the Academy of Sciences of the Repub­lic be­gan. By that time I ‘was fond of and worked with great en­thu­si­asm in a new di­rec­tion- the study of bound­ary sums for par­tial dif­fer­en­tial equa­tions of mixed type with two lines and dif­fer­ent or­ders of de­gen­er­acy. This was the con­tent of my can­di­date dis­ser­ta­tion the­sis, which I de­fended in 1986.

In 2000 I de­fended Ph.D. the­sis on the topic “To the the­ory of a mixed-type equa­tion with two lines and planes of de­gen­er­acy”, and in 2006 I was ap­pointed pro­fes­sor.

- And can you trans­late some­how the ti­tle of the doc­toral dis­ser­ta­tion into a pop­u­lar lan­guage?

- Yes I can, but it is not easy, it will take a long time. - Have you car­ried the love to the equa­tions through­out your life?

“It’s love for sci­ence, love for math­e­mat­ics”. I am al­ways in­spired by our great an­ces­tors, who made an in­valu­able con­tri­bu­tion to the de­vel­op­ment of sci­ence and world civ­i­liza­tion. - How many re­searches did you pub­lish?

- I did not specif­i­cally con­sider it, but not less than 170 - a monograph, teach­ing aids, sci­en­tific ar­ti­cles in na­tional and in­ter­na­tional edi­tions. - What does give you the greatest joy in your work now?

- First of all, th­ese are my stu­dents, young math­e­ma­ti­cians of our coun­try. Among them there are many can­di­dates of phys­i­cal and math­e­mat­i­cal sciences who work on doc­toral and PhD the­ses. I am end­lessly heart­ened by their work, en­thu­si­asm, de­sire to make their con­tri­bu­tion to sci­ence and to leave their mark. And I try to give them my ex­pe­ri­ence and knowl­edge.

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