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The celebrated Zariski Cancellation Problem asks as to when the existence of an isomorphism If the cancellation does not hold then

Adaptive side-lobe cancellation technology is an anti-jamming method commonly used in modern radars. In order to improve the jamming effect, it is necessary to study feasible jamming methods according to its characteristics. By analyzing the principle of adaptive side-lobe cancellation technology, this paper proposes a method that combines multi-directional jamming and correlated jamming. In order to verify the feasibility and advantages of this method, the simulation and analysis of the multi-machine interrupted-sampling cycle repeated jamming pattern signal against side-lobe cancellation system are carried out.

In-band full duplex (IBFD) is regarded as one of the most significant technologies for addressing the issue of spectrum scarcity in 5G and beyond systems. In the realization of practical IBFD systems, self-interference, i.e., the interference that the transmitter causes to the collocated receiver, poses a major challenge to antenna designers; it is a prerequisite for applying other self-interference cancellation (SIC) techniques in the analog and digital domains. In this paper, a comprehensive survey on SIC techniques in the antenna/propagation (AP) domain is provided and the pros and cons of each technique are studied. Opportunities and challenges of employing IBFD antennas in future wireless communications networks are discussed.

We study a Morita-equivalent version of the Zariski cancellation problem.

This paper provides a comprehensive theoretical derivation of the residual noise power and effective isotropic isolation (EII) signal models in baseband digital cancellation, aperture-level digital cancellation, and beamforming spatial cancellation models in simultaneous transmit and receive (STAR) arrays. We simulated and analyzed the isolation performance and self-interference (SI) noise cancellation of STAR systems using digital SI cancellation (SIC) and beamforming in a 32-element planar array. The simulation results show that in the absence of SIC or baseband digital SIC, the EII obtained by receive adaptive beamforming (ABF) is 20 dB higher than that obtained by transmit ABF. On the basis of aperture-level digital SIC, the EII obtained from transmit ABF and receive ABF is basically the same. The EII obtained by baseband digital SIC is 22.5 dB and 41.1 dB lower than that of transmit ABF and receive ABF, respectively. Therefore, baseband digital SIC technology is not required when using transmit ABF and receive ABF.

Reinforcement learning for multi-step reasoning with large language models (LLMs) typically relies on sparse terminal rewards, which creates a poorly conditioned credit-assignment problem: the final feedback is propagated uniformly across all intermediate decisions. This leads to high gradient variance, unstable training, and many ineffective updates, ultimately limiting sustained model improvement. We propose a counterfactual-comparison framework for credit assignment. For each input, the framework samples multiple reasoning trajectories and treats their differences as implicit approximations to alternative decisions. This yields an implicit process-level advantage estimator that converts sparse terminal rewards into step-sensitive learning signals. Building on this framework, we introduce Implicit Behavior Policy Optimization (IBPO), which substantially improves training stability and the performance ceiling on mathematical and code-reasoning benchmarks. Our results point to a promising direction for unlocking the reasoning potential of LLMs.

Purpose – This paper investigates cancellations and no-shows in hotel reservations using granular transaction data from a property management system. The aim is to identify typical behavioural patterns of guests who cancel their stays or fail to attend. Methodology/Design/Approach – A dataset of 33,263 reservations was analysed using the CHAID decision tree model. Classification included various nominal and continuous variables: reservation status, number of guests, length of stay, distribution channel, gross rate, rate type, lead time, and number of rooms. Findings – The analysis revealed that cancellations are more likely for reservations with long lead times and flexible cancellation policies. No-shows are more frequently associated with bookings at lower gross rates. Reservations made via intermediaries such as OTAs and wholesalers show higher cancellation and no-show rates compared to other channels. Originality of the research – The study’s originality stems from the use of detailed user transaction data, offering empirical evidence of customer behaviour in the hotel booking process. By analysing real operational data, the study contributes to a deeper understanding of cancellation and no-show behaviour, supporting more accurate forecasting and revenue management strategies in the hospitality industry.

This letter reports an 85 GHz low noise amplifier (LNA) employing derivative superposition based non‐linearity cancellation and a current re‐use topology. The LNA employs a two‐stage stacked architecture, each featuring neutralized differential pairs utilizing the same DC current. In derivative superposition, an auxiliary branch consisting of neutralized differential pairs cells is added in the LNA in parallel to stage 1 to ensure non‐linearity cancellation. Layout‐based capacitive neutralization is implemented to improve GMAX, resulting in simplified routing, reduced parasitics, and a more compact layout. The proposed LNA is fabricated in TSMC 28 nm CMOS process and achieves a peak gain of 8.4 dB at 84.2 GHz with a measured 3 dB bandwidth (BW3dB $\\text{BW}_{3\\text{dB}}$ ) from 79.4 to 92 GHz. The minimum measured noise figure is 12.8 dB. The LNA draws 34 mA of DC current from a 1.2 V supply. The highly linear LNA with IIP3 +6.5 dBm is tailored for automotive RADAR and 6G receivers. A high‐performance 85 GHz stacked low noise amplifier is presented, featuring derivative superposition based non‐linearity cancellation. The two‐stage stacked architecture incorporates neutralized differential pairs with an auxiliary branch in parallel to stage 1 for non‐linearity cancellation. Implemented in TSMC 28 nm CMOS, the low noise amplifier achieves 8.4 dB peak gain at 84.2 GHz with 12.6 GHz as 3‐dB bandwidth, drawing 34 mA from a 1.2 V supply. With IIP3 of +6.5 dBm, it is tailored for automotive RADAR and 6G receivers.

Using \\(E_8\\) bundles, we construct some new modular forms over \\(SL(2, Z)\\), \\(^0(2)\\) and \\(_0(2)\\) and get some new anomaly cancellation formulas of characteristic forms which generalize some anomaly cancellation formulas in [13].

Graphical small cancellation extends the classical small cancellation theory and provides a powerful method for constructing groups with interesting features. In the classical setting, C(3)-T(6) small cancellation complexes are known to admit locally CAT(0) metrics. In this paper, we construct locally CAT(0) metrics for graphical C(3)-T(6) complexes.