The Shortest-Known Paper Published in a Serious Math Journal: Two Succinct Sentences

My con­tri­bu­tion to this top­ic:

Short post, short papers, enjoy! LOG#170. The short­est papers ever: the list.

http://www.thespectrumofriemannium.com/2015/04/13/log170-the-shortest-papers-ever-the-list/

akso we see more aspects as say prof dr mircea orasanu and prof horia orasanu aspects as fol­low­ings
MATHEMATICS AND EDUCATION

ABSTRACT
]. In these approach­es one may derive covari­ant ver­sions of the Fokker-Planck equa­tion of Brown­ian motion in curved spaces. The math­e­mat­i­cal approach to path inte­grals uses sim­i­lar tech­niques [5]. The inher­ent ambi­gu­i­ties can be removed by demand­ing a cer­tain form for Schrödinger equa­tion of the sys­tem, which in curved space is have the Laplace-Bel­tra­mi oper­a­tor as an oper­a­tor for the kinet­ic ener­gy [2], with­out an addi­tion­al cur­va­ture scalar.

here we con­sid­er some as say prof dr mircea orasanu and prof horia orasanu as Rie­mann Hilbert prob­lem

sure as say prof dr mircea orasanu and prof horia orasanu as fol­lowed

GAUSS AND EULER
ABSTRACT
Let’s approach Leon­hard Euler and his work the same way. It will make things a whole lot eas­i­er.

If one is not a math­e­mati­cian (and except for a few of you out there, who is?), it’s going to be impos­si­ble to actu­al­ly under­stand why Euler was such a great man. Oth­er peo­ple will have to tell us, and we should prob­a­bly believe them.

in these sit­u­a­tions we con­sid­er that thus as how meet and as look prof dr mircea orasanu and prof drd horia orasanu as fol­lowed with
PROBLEM OF OPEN CULTURE AND APPLICATIONS
ABSTRACT
In gen­er­al, par­tial dif­fer­en­tial equa­tions are dif­fi­cult to solve, but tech­niques have been devel­oped for sim­pler class­es of equa­tions called lin­ear, and for class­es known loose­ly as “almost” lin­ear, in which all deriv­a­tives of an order high­er than one occur to the first pow­er and their coef­fi­cients involve only the inde­pen­dent vari­ables.
Many phys­i­cal­ly impor­tant par­tial dif­fer­en­tial equa­tions are sec­ond-order and lin­ear. For exam­ple:
uxx + uyy = 0 (two-dimen­sion­al Laplace equa­tion)
uxx = ut (one-dimen­sion­al heat equa­tion)
uxx − uyy = 0 (one-dimen­sion­al wave equa­tion)

as an impor­tant ques­tion of the above are men­tioned the F. VIETTE , KRONECKER The­o­rem and oth­er as are observed in and for prof dr mircea orasanu and prof drd horia orasanu as fol­lowed
PARTIAL DIFFERENTIAL EQUATIONS AND ANALYTICAL CALCULUS
ABSTRACT
is very ped­a­gog­i­cal thes ques­tions and Par­tial dif­fer­en­tial equa­tion, in math­e­mat­ics, equa­tion relat­ing a func­tion of sev­er­al vari­ables to its par­tial deriv­a­tives. A par­tial deriv­a­tive of a func­tion of sev­er­al vari­ables express­es how fast the func­tion changes when one of its vari­ables is changed, the oth­ers being held con­stant (com­pare ordi­nary dif­fer­en­tial equa­tion). The par­tial deriv­a­tive of a func­tion is again a func­tion, and, if f(x, y) denotes the orig­i­nal func­tion of the vari­ables x and y, the par­tial deriv­a­tive with respect to x—i.e., when only x is allowed to vary—is typ­i­cal­ly writ­ten as fx(x, y) or ∂f/∂x. The oper­a­tion of find­ing a par­tial deriv­a­tive can be applied to a func­tion that is itself a par­tial deriv­a­tive of anoth­er func­tion to get what is called a sec­ond-order par­tial derivative.In gen­er­al, par­tial dif­fer­en­tial equa­tions are dif­fi­cult to solve, but tech­niques have been devel­oped for sim­pler class­es of equa­tions called lin­ear, and for class­es known loose­ly as “almost” lin­ear, in which all deriv­a­tives of an order high­er than one occur to the first pow­er and their coef­fi­cients involve only the inde­pen­dent vari­ables.
Many phys­i­cal­ly impor­tant par­tial dif­fer­en­tial equa­tions are sec­ond-order and lin­ear. For exam­ple:

oth­er sit­u­a­tions appear for as con­sid­er­ing the future of teacher edu­ca­tion at the present time, I believe that it is rel­e­vant to con­sid­er the wider social and polit­i­cal con­text in which schools and insti­tu­tions of teacher edu­ca­tion are placed at this time observed prof dr mircea orasanu

these aspects appear with some aspects as since that prof dr mircea orasanu and prof drd horia orasanu con­cern more and many as fol­lowed for Louis Uni­ver­si­ty in domain Col­lo­qui­um of com­plex poten­tial and Rie­mann Hilnert prob­lem lead by I and to COLLEGE LYCEUM MAGNA
Effect of lim­it­ed T
(3) Dose DFT give for every f ?
No! only dis­crete fre­quen­cies.
DFT as an esti­mate for X(f): even worse than due to the lim­it­ed fre­quen­cy res­o­lu­tion.

1. Effect of sam­pling fre­quen­cy (or num­ber of points) on accu­ra­cy when T is giv­en: Exam­ple
use for
2. Effect of T (win­dow size)
Com­pare and for

there are many ques­tions in His­to­ry or sci­ence that are observed by prof dr mircea orasanu and prof drd horia orasanu and as fol­lowed for estab­lised of impor­tant sit­u­a­tions and chap­ter of scle­ronoo­mous devel­op­ments and oth­er so a sim­ple pen­du­lum is a sys­tem com­posed of a weight and a string. The string is attached at the top end to a piv­ot and at the bot­tom end to a weight. Being inex­ten­si­ble, the string’s length is a con­stant. There­fore, this sys­tem is scle­ronomous; it obeys scle­ro­nom­ic con­straint
x 2 + y 2 − L = 0 , {\dis­playstyle {\sqrt {x^{2}+y^{2}}}-L=0\,\!,} {\sqrt {x^{2}+y^{2}}}-L=0\,\!,
where ( x , y ) {\dis­playstyle (x,y)\,\!} (x,y)\,\! is the posi­tion of the weight and L {\dis­playstyle L\,\!} L\,\! is length of the string.
A sim­ple pen­du­lum with oscil­lat­ing piv­ot point
Take a more com­pli­cat­ed exam­ple. Refer to the next fig­ure at right, Assume the top end of the string is attached to a piv­ot point under­go­ing a sim­ple har­mon­ic motion
x t = x 0 cos ⁡ ω t , {\dis­playstyle x_{t}=x_{0}\cos \omega t\,\!,} x_{t}=x_{0}\cos \omega t\,\!,
where x 0 {\dis­playstyle x_{0}\,\!} x_{0}\,\! is ampli­tude, ω {\dis­playstyle \omega \,\!} \omega \,\! is angu­lar fre­quen­cy, and t {\dis­playstyle t\,\!} t\,\! is time.

in many sit­u­a­tions con­cern­ing the ped­a­gogy appear for prof dr mircea orasanu and prof drd horia orasanu impor­tant sit­u­a­tions due these occa­sion that per­mit­ted many con­se­quences

for most impor­tant aspects are pre­sent­ed oth­er sit­u­a­tions so that observed prof dr mircea and prof dr d horia orasanu that remarked the form of appli­ca­tions and fol­lowed that then so lead to CONSTRAINTS prob­lem and thus . Loco­mo­tion of a snake-like struc­ture in accor­dance with the ser­penoid curve, i.e. lat­er­al undu­la­tion, is achieved if the joints of the robot move accord­ing to the ref­er­ence joint tra­jec­to­ries in the form of a sinu­soidal func­tion with spec­i­fied ampli­tude, fre­quen­cy, and phase shift. In par­tic­u­lar, using the fore­go­ing defined new states, we define a con­straint func­tion for the ith joint of the snake robot by
Φi = αsin(η + (i − 1)δ) + ϕo
(45)
where i∈{1,…,N−1}, α denotes the ampli­tude of the sinu­soidal joint motion, and δ is a phase shift that is used to keep the joints out of phase. More­over, ϕo is an off­set val­ue that is iden­ti­cal for all of the joints. It was illus­trat­ed in [16] how the off­set val­ue ϕo affects the ori­en­ta­tion of the snake robot in the plane. Build­ing fur­ther on this insight, we con­sid­er the sec­ond-order time deriv­a­tive of ϕo in the form of a dynam­ic com­pen­sator, which will be used to con­trol the ori­en­ta­tion of the robot. In par­tic­u­lar, through this con­trol term, we mod­i­fy the ori­en­ta­tion of the robot in accor­dance with a ref­er­ence ori­en­ta­tion. This will be done by adding an off­set angle to the ref­er­ence tra­jec­to­ry of each joint. We will show that this will steer the posi­tion of the CM of the robot towards the desired path. The con­straint func­tion (45) is dynam­ic, since it depends on the solu­tion of a dynam­ic com­pen­sator.
Vir­tu­al holo­nom­ic con­straint for the head link angle
In this sub­sec­tion, we define a con­straint func­tion for the head angle of the robot. In par­tic­u­lar, we use a line-of-sight (LOS) guid­ance law as the ref­er­ence angle for the head link. LOS guid­ance is a much-used method in marine con­trol sys­tems (see, e.g. [27]). In gen­er­al, guid­ance-based con­trol strate­gies are based on defin­ing a ref­er­ence head­ing angle for the vehi­cle through a guid­ance law and design­ing a con­troller to track this angle [27]. Moti­vat­ed by marine con­trol lit­er­a­ture, in [17] based on a sim­pli­fied mod­el of the snake robot, using cas­cade sys­tems the­o­ry, it was proved that if the head­ing angle of the snake robot was con­trolled to the LOS angle, then also the posi­tion of the CM of the robot would con­verge to the desired path. We will show that a sim­i­lar guid­ance-based con­trol strat­e­gy can suc­cess­ful­ly steer the robot towards the desired path. How­ev­er, we per­form the mod­el-based con­trol design based on a more accu­rate mod­el of the snake robot which does not con­tain the sim­pli­fy­ing assump­tions of [17] which are valid for small joint angles.
To define the guid­ance law, with­out loss of gen­er­al­i­ty, we assign the glob­al coor­di­nate sys­tem such that the glob­al x‑axis is aligned with the desired path. Con­se­quent­ly, the posi­tion of the CM of the robot along the y‑axis, denot­ed by py, defines the short­est dis­tance between the robot and the desired path, often referred to as the cross-track error. In order to solve the path fol­low­ing prob­lem, we use the LOS guid­ance law as a vir­tu­al holo­nom­ic con­straint, which defines the desired head angle as a func­tion of the cross-track error as
ΦN=−tan−1(pyΔ)

in these must con­sid­er mod­u­lar forms as observed prof dr mircea orasanu and prof drd horia orasanu and con­cern­ing and fol­lowed these used for ELLIPTICAL and inte­grals that are used for devel­oped forms