A New Class of Biased Linear Estimators in Deficient-rank Linear Models

In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.

Orientation Bias of Self-Assembled Alkanes and Their Derivatives Under Dynamic Lateral Nanoconfinement Conditions

Self-assembled molecular networks(SAMNs)formed on crystalline solid substrates result from the spontaneous arrangement of individual molecules into structured patterns.The interaction between molecules and the substrate leads to a nonrandom orientation of SAMNs with respect to the substrate’s lattice.In the case of graphite,the sixfold rotational symmetry of the substrate results in an equivalent rotational degeneracy in the orientation of SAMNs.In this study,we explored how nanoconfinement,that is,the restriction of SAMN formation to nanometersized areas,known as nanocorrals,could impact and potentially alleviate the orientational degeneracy of SAMNs,with emphasis on the influence of molecule symmetry,size,and intermolecular interactions.To this end,we investigated the orientation distribution of n-alkanes and functionalized alkanes within nanocorrals,which were fabricated using scanning tunneling microscopy lithography(nanoshaving).We observed lifting of orientational degeneracy for long alkanes,contrary to shorter alkanes,which did not exhibit this orientation preference.Notably,functionalized alkanes with hydrogen bonding groups demonstrated preferential alignment regardless of length,highlighting the significance of stabilizing intermolecular interactions in the alignment process.This study discussed the underlying principles of the molecular packing process and shed light on the complexity of molecular self-assembly in nanoconfined spaces.

Projection of hydrothermal condition in Central Asia under four SSP-RCP scenarios

Hydrothermal condition is mismatched in arid and semi-arid regions,particularly in Central Asia(including Kazakhstan,Kyrgyzstan,Tajikistan,Uzbekistan,and Turkmenistan),resulting many environmental limitations.In this study,we projected hydrothermal condition in Central Asia based on bias-corrected multi-model ensembles(MMEs)from the Coupled Model Intercomparison Project Phase 6(CMIP6)under four Shared Socioeconomic Pathway and Representative Concentration Pathway(SSP-RCP)scenarios(SSP126(SSP1-RCP2.6),SSP245(SSP2-RCP4.5),SSP460(SSP4-RCP6.0),and SSP585(SSP5-RCP8.5))during 2015-2100.The bias correction and spatial disaggregation,water-thermal product index,and sensitivity analysis were used in this study.The results showed that the hydrothermal condition is mismatched in the central and southern deserts,whereas the region of Pamir Mountains and Tianshan Mountains as well as the northern plains of Kazakhstan showed a matched hydrothermal condition.Compared with the historical period,the matched degree of hydrothermal condition improves during 2046-2075,but degenerates during 2015-2044 and 2076-2100.The change of hydrothermal condition is sensitive to precipitation in the northern regions and the maximum temperatures in the southern regions.The result suggests that the optimal scenario in Central Asia is SSP126 scenario,while SSP585 scenario brings further hydrothermal contradictions.This study provides scientific information for the development and sustainable utilization of hydrothermal resources in arid and semi-arid regions under climate change.

Bias dependence of a deep submicron NMOSFET response to total dose irradiation

Deep submicron n-channel metal-oxide-semiconductor field-effect transistors （NMOSFETs） with shallow trench isolation （STI） are exposed to ionizing dose radiation under different bias conditions. The total ionizing dose radiation induced subthreshold leakage current increase and the hump effect under four different irradiation bias conditions including the worst case （ON bias） for the transistors are discussed. The high electric fields at the corners are partly responsible for the subthreshold hump effect. Charge trapped in the isolation oxide, particularly at the Si/SiO2 interface along the sidewalls of the trench oxide creates a leakage path, which becomes a dominant contributor to the offstate drain-to-source leakage current in the NMOSFET. Non-uniform charge distribution is introduced into a threedimensional （3D） simulation. Good agreement between experimental and simulation results is demonstrated. We find that the electric field distribution along with the STI sidewall is important for the radiation effect under different bias conditions.

Adaptive Unified Biased Estimators of Parameters in Linear Model

To tackle multi collinearity or ill-conditioned design matrices in linear models, adaptive biased estimators such as the time-honored Stein estimator, the ridge and the principal component estimators have been studied intensively. To study when a biased estimator uniformly outperforms the least squares estimator, some sufficient conditions are proposed in the literature. In this paper, we propose a unified framework to formulate a class of adaptive biased estimators. This class includes all existing biased estimators and some new ones. A sufficient condition for outperforming the least squares estimator is proposed. In terms of selecting parameters in the condition, we can obtain all double-type conditions in the literature.

A Note on Convergence of a Sequence and Its Applications to Geometry of Banach Spaces

The purpose of this note is to point out several obscure places in the results of Ahmed and Zeyada [J. Math. Anal. Appl. 274 (2002) 458-465]. In order to rectify and improve the results of Ahmed and Zeyada, we introduce the concepts of locally quasi-nonexpansive, biased quasi-nonexpansive and conditionally biased quasi-nonexpansive of a mapping w.r.t. a sequence in metric spaces. In the sequel, we establish some theorems on convergence of a sequence in complete metric spaces. As consequences of our main result, we obtain some results of Ghosh and Debnath [J. Math. Anal. Appl. 207 (1997) 96-103], Kirk [Ann. Univ. Mariae Curie-Sklodowska Sec. A LI.2, 15 (1997) 167-178] and Petryshyn and Williamson [J. Math. Anal. Appl. 43 (1973) 459-497]. Some applications of our main results to geometry of Banach spaces are also discussed.