Lately, Ellingsen et al created a new concept by making minor changes on the old concept of (multiplicative) differential. This new definition which has potential to be capable of extending differential cryptanalysis in a completely new way is named as c-differential and brought with it the concept of c-differential uniformity. We examlify that how some known functions' behaviour, especially inverse function, would be under this extended differential. The main purpose of this thesis is to observe how the swapped inverse function, which is one of the variety of ways to modify the binary inverse function, impacts the function's c-differential uniformity. In this thesis, we proposed a new theorem including the new characterization of the $(0,\alpha)$-swapped inverse function in even characteristic under this new concept, $x^{2^n-2}+x^{2^n-1}/\alpha+(x-\alpha)^{2^n-1}/\alpha$ on $\matbb{F}_{2^n}$, and reached two conclusions for all $c\neq1$: we prove that its c-differential uniformity value can take 1,2,3 and 4 and attains its maximum value 4 under two special conditions satisfied by the trace mapping.


Nonlinear dynamic modeling of gear-shaft-disk-bearing systems using finite elements and describing functions
Maliha, R; Dogruer, CU; Özgüven, Hasan Nevzat (ASME International, 2004-05-01)
This study presents a new nonlinear dynamic model for a gear-shaft-disk-bearing system. A nonlinear dynamic model of a spur gear pair is coupled with linear finite element models of shafts carrying them, and with discrete models of bearings and disks. The nonlinear elasticity term resulting from backlash is expressed by a describing function, and a method developed in previous studies to determine multi harmonic responses of nonlinear multi-degree-of-freedom systems is employed for the solution. The excitat...
A Feedback Quantization Scheme Leveraging Fairness and Throughput for Heterogeneous Multi-User Diversity Systems
SOYDAN, Yusuf; Candan, Çağatay (Institute of Electrical and Electronics Engineers (IEEE), 2010-06-01)
We propose a feedback quantization scheme for downlink multiuser diversity systems. The scheme is designed for heterogeneous users, i.e., users operating under different levels of mean signal-to-noise ratios (SNRs). The proposed scheme equally distributes the channel access time to user clusters and, at the same time, maximizes the sum-rate capacity under equal-channel-access-time constraint. The method is compared to a normalized SNR scheduler, full-feedback scheduler, and finite-rate feedback scheduler wi...
Co-Design Practice in Industrial Design Education in Turkey A Participatory Design Project
Yalman Yıldırım, Zeynep (2015-01-01)
The evolution in design research has shifted from a user-centered design approach to co-design approach. With co-designing, roles of designers and users have changed. In growing co-creation and co-design notions, user is seen as a partner, not as a passive object of study. In current undergraduate industrial design education in Turkey, user research is done in limited steps during design process. User observations that are required for students during their design processes are done outside of studio course...
Chaotic breather formation, coalescence, and evolution to energy equipartition in an oscillatory chain
Mirnov, VV; Lichtenberg, AJ; Guclu, H (2001-10-01)
We study the formation and evolution of chaotic breathers (CBs) on the Fermi-Pasta-Ulam oscillator chain with quartic nonlinearity (FPU-beta system). Starting with most of the energy in a single high-frequency mode, the mode is found to breakup on a fast time scale into a number of spatially localized structures (CBs) which, on a slower time scale, coalesce into a single CB. On a usually longer time scale, depending strongly on the energy, the CB gives up its energy to lower frequency modes, approaching ene...
Cooperation control of three UAV’s for Aerial Rescue and Aerial Retrieval
Erkmen, Aydan Müşerref; Yavrucuk, İlkay (IEEE; 2009-12-14)
In this paper two new conceptual robotic system designs, called 'aerial-retrieval' and 'aerial-rescue' are presented and demonstrated by simulation results. The Unmanned air vehicles (UAV) used in this design are thrust vector controlled robotic systems. The 'aerial-retrieval' concept aims at entrapping and retrieving a (lost) floating object in the air. The second concept, 'aerial-rescue' aims at rescuing a free falling object (e.g. a person) in the air using a stretched net attached to the UAV's. Position...
Citation Formats
B. ÜNVER, “SOME STUDIES ON c-DIFFERENTIAL UNIFORMITY OF SWAPPED INVERSE FUNCTION,” M.S. - Master of Science, Middle East Technical University, 2021.