Pub Date : 2023-11-04DOI: 10.1134/S1990478923030092
A. A. Kosov, E. I. Semenov
The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationary solutions are found on the invariant set of the zero level of the area integral, and their stability is analyzed. For the case where the suspension point coincides with the center of mass and the action of a gyroscopic moment is of a special type, integration by quadratures is performed.
{"title":"On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat","authors":"A. A. Kosov, E. I. Semenov","doi":"10.1134/S1990478923030092","DOIUrl":"10.1134/S1990478923030092","url":null,"abstract":"<p> The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationary\u0000solutions are found on the invariant set of the zero level of the area integral, and their stability is\u0000analyzed. For the case where the suspension point coincides with the center of mass and the\u0000action of a gyroscopic moment is of a special type, integration by quadratures is performed.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-04DOI: 10.1134/S1990478923030055
D. A. Bykov, N. A. Kolomeec
Bent functions at the minimum distance ( 2^n ) from a given bent function of ( 2n ) variables belonging to the Maiorana–McFarland class ( mathcal {M}_{2n} ) are investigated. We provide a criterion for a function obtained using the addition of the indicator of an ( n )-dimensional affine subspace to a given bent function from ( mathcal {M}_{2n} ) to be a bent function as well. In other words, all bent functions at the minimum distance from a Maiorana–McFarland bent function are characterized. It is shown that the lower bound ( 2^{2n+1}-2^n ) for the number of bent functions at the minimum distance from ( f in mathcal {M}_{2n} ) is not attained if the permutation used for constructing ( f ) is not an APN function. It is proved that for any prime ( ngeq 5 ) there exist functions in ( mathcal {M}_{2n} ) for which this lower bound is accurate. Examples of such bent functions are found. It is also established that the permutations of EA-equivalent functions in ( mathcal {M}_{2n} ) are affinely equivalent if the second derivatives of at least one of the permutations are not identically zero.
{"title":"On a Lower Bound for the Number of Bent Functions at the Minimum Distance from a Bent Function in the Maiorana–McFarland Class","authors":"D. A. Bykov, N. A. Kolomeec","doi":"10.1134/S1990478923030055","DOIUrl":"10.1134/S1990478923030055","url":null,"abstract":"<p> Bent functions at the minimum distance\u0000<span>( 2^n )</span> from a given bent function of\u0000<span>( 2n )</span> variables belonging to the Maiorana–McFarland class\u0000<span>( mathcal {M}_{2n} )</span> are investigated. We provide a criterion for a function obtained using the\u0000addition of the indicator of an\u0000<span>( n )</span>-dimensional affine subspace to a given bent function from\u0000<span>( mathcal {M}_{2n} )</span> to be a bent function as well. In other words, all bent functions at the\u0000minimum distance from a Maiorana–McFarland bent function are characterized. It is shown that\u0000the lower bound\u0000<span>( 2^{2n+1}-2^n )</span> for the number of bent functions at the minimum distance from\u0000<span>( f in mathcal {M}_{2n} )</span> is not attained if the permutation used for constructing\u0000<span>( f )</span> is not an APN function. It is proved that for any prime\u0000<span>( ngeq 5 )</span> there exist functions in\u0000<span>( mathcal {M}_{2n} )</span> for which this lower bound is accurate. Examples of such bent functions are\u0000found. It is also established that the permutations of EA-equivalent functions in\u0000<span>( mathcal {M}_{2n} )</span> are affinely equivalent if the second derivatives of at least one of the\u0000permutations are not identically zero.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}