On the smoothness of Orlicz sequence spaces equipped with Orlicz norm

We give a criterion of smoothness of Orlicz sequence spaces with Orlicz norm

Case report: BCR-ABL-positive acute lymphoblastic leukemia with bone destruction: a treatment dilemma

Although bone destruction and hypercalcemia without acute peripheral blast BCR-ABL-positive acute lymphoblastic leukemia (ALL) have been reported in children, they are rare in adults. Herein, we describe a case of BCR-ABL positive ALL with a triploid karyotype, WT1, and CDKN2A mutations with hypercalcemia and bone destruction as the first manifestations. Complete remission (CR) was achieved by induction chemotherapy. BCR-ABL turned negative after treatment with dasatinib. However, computed tomography and whole-body bone scan showed extensive bone destruction. Additionally, bone biopsy showed leukemic infiltration. After treatment with dasatinib and VMCP, leukemia recurred with positive BCR-ABL. The T315I mutation occurred. The patient was surgically diagnosed with calculous cholecystitis and achieved CR2 by postoperative orebatinib and VP regimens. Later, the patient died due to a severe pulmonary infection. BCR-ABL-positive ALL with bone destruction is rare and difficult to control using tyrosine kinase inhibitor chemotherapy alone. Therefore, further exploration of more effective treatments is needed

The Nearest Neutron Star Candidate in a Binary Revealed by Optical Time-domain Surveys

Recent studies have revealed the global deposition on Earth of radioactive elements (e.g., $^{60}$Fe) resulting from the metal-enriched ejecta of nearby (within $\sim 100$ pc) supernova explosions. The majority of neutron stars in our Solar neighborhood remain to be discovered. Here we report the discovery of the nearest ($127.7 \pm 0.3$ pc) neutron star candidate in the single-lined spectroscopic binary LAMOST J235456.76+335625.7 (hereafter J2354). Utilizing the multi-epoch spectra and high-cadence periodic light curves, we measure the mass of the visible star ($M_{\rm vis}=0.70\pm 0.05\ M_{\odot}$) and determine the mass function of the invisible object $f(M)=0.525 \pm 0.004\ M_{\odot}$, i.e., the mass of the unseen compact object is $M_{\rm inv} \geq 1.26 \pm 0.03\ M_{\odot}$. The excess UV emission due to a hot supramassive white dwarf is absent. Hence, it is likely that J2354 harbors a neutron star. J2354 is X-ray dim (the$0.1$--$2.4$keV luminosity$<10^{30}\ {\rm erg\ s^{-1}}$) since it is not detected in the ROSAT all-sky surveys in X-ray. One-hour exceptionally sensitive radio follow-up observations with FAST, the largest single-dish radio telescope, failed to reveal any radio pulsating signals (the potential pulse power at$1.4$GHz is$<6.8\times 10^{23}\ {\rm erg\ s^{-1}}$). Hence, the neutron star candidate in J2354 can only be discovered via our time-resolved observations. The alternative scenario involving a nearby supramassive cold white dwarf cannot be fully excluded. Our discovery demonstrates a promising way to unveil the missing population of backyard inactive neutron stars or supramassive cold white dwarfs in binaries by exploring the optical time domain, thereby facilitating understanding of the supernovae explosion and metal-enrichment history in our Solar neighborhood.Comment: 35 pages, 8 figures, to be submitte

K-extreme point of generalized orlicz sequence spaces with Luxemburg norm

In this paper,we give necessary and sufficient conditions in order that a point $u\in S(l_{({\it \Phi})})$ is a k-extreme point in generalized Orlicz sequence spaces equipped with the Luxemburg norm, combing the methods used in classical Orlicz spaces and new methods introduced especially for generalized ones. The results indicate the difference between the classical Orlicz spaces and generalized Orlicz spaces

On the uniformly normal structure of Orlicz spaces with Orlicz norm

summary:We prove that in Orlicz spaces endowed with Orlicz norm the uniformly normal structure is equivalent to the reflexivity

Weakly compact sets in Orlicz sequence spaces

summary:We combine the techniques of sequence spaces and general Orlicz functions that are broader than the classical cases of $N$-functions. We give three criteria for the weakly compact sets in general Orlicz sequence spaces. One criterion is related to elements of dual spaces. Under the restriction of $\lim _{u\rightarrow 0} M(u)/u=0$, we propose two other modular types that are convenient to use because they get rid of elements of dual spaces. Subsequently, by one of these two modular criteria, we see that a set $A$ in Riesz spaces $l_p$ $(1 < p < \infty )$ is relatively sequential weakly compact if and only if it is normed bounded, that says $\sup _{u\in A}\sum _{i=1}^{\infty } |u(i)|^p < \nobreak \infty$. The result again confirms the conclusion of the Banach-Alaoglu \hbox {theorem}