A Multivalued Version of the Block–Sharkovsky Theorem Applicable to Differential Equations on the Circle

2018 ◽  
Vol 28 (11) ◽  
pp. 1850142
Author(s):  
Jan Andres ◽  
Karel Pastor
Keyword(s):  
Differential Equations ◽  
The Other ◽  
Other Hand ◽  
Random Differential Equations ◽  
Standard Block ◽  
Periodic Dynamics ◽  
Differential Equations And Inclusions

A multivalued version of the well-known (Sharkovsky type) Block cycle coexistence theorem is, on the basis of our former results, completed and applied to differential equations and inclusions. The deterministic results are also randomized which allows us, besides other things, to eliminate some exceptional absent periodic dynamics. In this way, instead of at most two possible deterministic exceptional cases (w.r.t. the standard Block theorem), only one possible random exception can occur, provided the forcing period [Formula: see text], [Formula: see text]. On the other hand, the application to random differential equations and inclusions is not so effective in general.

scholarly journals Researches in physical astronomy

1837 ◽  
Vol 3 ◽  
pp. 128-129
Keyword(s):  
Differential Equations ◽  
The Other ◽  
Disturbing Function ◽  
Direct Integration ◽  
Planetary Theory ◽  
The Moon ◽  
Disturbing Force ◽  
Other Hand ◽  
The Stability ◽  
The One

The present paper contains some further developments of the theory of the moon, which are given at length, in order to save the trouble of the calculator, and to avoid the danger of mistake. The author remarks, that while it seems desirable, on the one hand, to introduce into the science of physical astronomy a greater degree of uniformity, by bringing to perfection a theory of the moon founded on the integration of the equations employed in the planetary theory, it is also no less important, on the other hand, to complete, in the latter, the method hitherto applied solely to the periodic inequalities. Hi­therto those terms in the disturbing function which give rise to the secular inequalities, have been detached, and the stability of the system has been inferred by means of the integration of certain equations, which are linear when the higher powers of the eccentri­cities are neglected and from considerations founded on the varia­tion of the elliptic constants. But the author thinks that the stability of the system may be inferred also from the expressions which result at once from the direct integration of the differential equations. The theory, he states, may be extended, without any analytical difficulty, to any power of the disturbing force, or of the eccentricities, ad­mitting the convergence of the series; nor does it seem to be limited by the circumstance of the planet’s moving in the same direction.

scholarly journals Some types of first order fractional differential equations and their applications

2021 ◽  
Vol 268 ◽  
pp. 01073
Author(s):  
Chiihuei Yu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Chain Rule ◽  
The Other ◽  
General Solutions ◽  
First Order ◽  
Other Hand ◽  
Fractional Differential

This paper uses a new multiplication of fractional functions and chain rule for fractional derivatives, regarding the Jumarie type of modified Riemann-Liouville fractional derivatives to obtain the general solutions of four types of first order fractional differential equations. On the other hand, some examples are proposed to illustrate our results.

On Partial Differential Equations in a Field of Prime Characteristic

1955 ◽  
Vol 7 ◽  
pp. 539-542 ◽  
Author(s):  
Arno Jaeger
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Prime Number ◽  
The Other ◽  
Prime Characteristic ◽  
Classical Analysis ◽  
Partial Differential ◽  
Other Hand ◽  
Algebraic Theories

In classical analysis ordinary differential equations and partial differential equations are distinct concepts, and the transition from one derivation to several partial derivations changes some of their properties distinctly. On the other hand, the algebraic theories of modified ordinary and partial differential equations (5; 6), based on the differentiations in the sense of Hasse (2) and Schmidt (3) and the multidifferentiations in the sense of Jaeger (4), turn out to be strikingly similar in the case of fields of prime number characteristic.

Coexistence of Random Subharmonic Solutions of Random Impulsive Differential Equations and Inclusions on a Circle

2020 ◽  
Vol 30 (10) ◽  
pp. 2050152
Author(s):  
Jan Andres
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Differential Inclusions ◽  
Impulsive Differential Equations ◽  
Subharmonic Solutions ◽  
Random Differential Equations ◽  
Random Impulses ◽  
Differential Equations And Inclusions

The coexistence of random periodic solutions with various periods (i.e. subharmonics) is proved to random differential equations on a circle with random impulses of all integer orders. One of the theorems is also extended to random differential inclusions on a circle with multivalued deterministic impulses. These results can be roughly characterized as a further application of the randomized Sharkovsky type theorems to random impulsive differential equations and inclusions on a circle.

scholarly journals Determining a Particular Solution for N-th Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following Form ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx

2020 ◽  
Vol 26 (3) ◽  
pp. 49-54
Author(s):  
Vasile Căruţaşu ◽  
Alexandru Hampu
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
The Other ◽  
Free Term ◽  
Order Linear ◽  
Other Hand ◽  
Constant Coefficients ◽  
Particular Solution ◽  
Linear Differential ◽  
The Way

AbstractA particular solution for the n-th order linear differential equations with constant coefficients that are free of term such as P(x)· ea·x ·cosnx or/and Q(x)·eb·x· sinnx, n∈ N, can be determined based on two elements: the way in which cosnx and sinnx can develop, and, on the other hand on the way a particular solution for the free terms P(x) ·ea·x·cosnx or/and Q(x)·eb·x·sinmx, n ∈N is sought. We can, of course, write the way a particular solution looks also in the case we have a combination of the two terms or more terms of this kind.

scholarly journals Determining a Particular Solution for Systems of Linear Differential Equations with Constant Coefficients that Have on the Column of Free Terms Functions Such As ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx

2020 ◽  
Vol 26 (3) ◽  
pp. 55-64
Author(s):  
Vasile Căruţaşu ◽  
Ioan Virca
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
The Other ◽  
Other Hand ◽  
Constant Coefficients ◽  
Particular Solution ◽  
Linear Differential ◽  
The Way

AbstractThe determination of a particular solution for the systems of linear differential equations with constant coefficients that have on the column of free terms functions such as ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx, or/and eb·x·Q(x) sinnx, n ∈ N, is based on the expansion of cosn x and sinn x, and, on the other hand, on how a particular solution for a column of free terms with functions such as ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx, n ∈ N, looks like. We can also write the way a particular solution looks like when we have a combination of two or more functions on the form ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx, n ∈ N in the column of free terms.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

Life Beyond 1MeV

1980 ◽  
Vol 38 ◽  
pp. 30-33
Author(s):  
K.H. Westmacott
Keyword(s):  
Electron Microscopy ◽  
Past Experience ◽  
The Other ◽  
Good Case ◽  
Other Hand ◽  
The U.S

Life beyond 1MeV – like life after 40 – is not too different unless one takes advantage of past experience and is receptive to new opportunities. At first glance, the returns on performing electron microscopy at voltages greater than 1MeV diminish rather rapidly as the curves which describe the well-known advantages of HVEM often tend towards saturation. However, in a country with a significant HVEM capability, a good case can be made for investing in instruments with a range of maximum accelerating voltages. In this regard, the 1.5MeV KRATOS HVEM being installed in Berkeley will complement the other 650KeV, 1MeV, and 1.2MeV instruments currently operating in the U.S. One other consideration suggests that 1.5MeV is an optimum voltage machine – Its additional advantages may be purchased for not much more than a 1MeV instrument. On the other hand, the 3MeV HVEM's which seem to be operated at 2MeV maximum, are much more expensive.

Can the Academic Self-Concept be Positive and Realistic?

2005 ◽  
Vol 19 (3) ◽  
pp. 129-132 ◽  
Author(s):  
Reimer Kornmann
Keyword(s):  
Academic Performance ◽  
Opposite Effect ◽  
Self Esteem ◽  
Point Of View ◽  
The Other ◽  
Self Concept ◽  
High Ability ◽  
Self Image ◽  
Other Hand

Summary: My comment is basically restricted to the situation in which less-able students find themselves and refers only to literature in German. From this point of view I am basically able to confirm Marsh's results. It must, however, be said that with less-able pupils the opposite effect can be found: Levels of self-esteem in these pupils are raised, at least temporarily, by separate instruction, academic performance however drops; combined instruction, on the other hand, leads to improved academic performance, while levels of self-esteem drop. Apparently, the positive self-image of less-able pupils who receive separate instruction does not bring about the potential enhancement of academic performance one might expect from high-ability pupils receiving separate instruction. To resolve the dilemma, it is proposed that individual progress in learning be accentuated, and that comparisons with others be dispensed with. This fosters a self-image that can in equal measure be realistic and optimistic.

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