Non-degeneracy of single-peak solutions to a Kirchhoff equation

2021 ◽  
pp. 1-7
Author(s):  
Jiahong Yan ◽  
Jing Yang
2020 ◽  
Vol 91 (3) ◽  
pp. 30901
Author(s):  
Yibo Tang ◽  
Longhui He ◽  
Jianming Xu ◽  
Hailang He ◽  
Yuhan Li ◽  
...  

A dual-band microwave metamaterial absorber with single-peak regulation and wide-angle absorption has been proposed and illustrated. The designed metamaterial absorber is consisted of hollow-cross resonators, solid-cross resonators, dielectric substrate and metallic background plane. Strong absorption peak coefficients of 99.92% and 99.55% are achieved at 8.42 and 11.31 GHz, respectively, which is basically consistent with the experimental results. Surface current density and changing material properties are employed to illustrate the absorptive mechanism. More importantly, the proposed dual-band metamaterial absorber has the adjustable property of single absorption peak and could operate well at wide incidence angles for both transverse electric (TE) and transverse magnetic (TM) waves. Research results could provide and enrich instructive guidances for realizing a single-peak-regulation and wide-angle dual-band metamaterial absorber.


1988 ◽  
Vol 41 (9) ◽  
pp. 1425 ◽  
Author(s):  
TG Appleton ◽  
JR Hall ◽  
SF Ralph ◽  
CSM Thompson

Palladium(II) ammine complexes enriched in 15N give sharp singlets in their 15N n.m.r . spectra. The 15N chemical shifts depend primarily on the trans donor atom, in a qualitatively similar way to those for platinum(II) ammine complexes. A dimethylformamide solution of Pd(NH3)2Cl2 prepared in the usual way gave a single peak, consistent with the presence of only one isomer (trans). Reactions of increasing amounts of aqueous perchloric acid with Pd(NH3)42+ allowed peaks to be identified for Pd(NH3)3(H2O)2+, cis -Pd(NH3)2(H2O)22+ and Pd(NH3)(H2O)32+. The initial product of the reaction of trans-Pd(NH3)2Cl2 with silver ion is trans-Pd(NH3)2(H2O)22+, which rapidly disproportionates to Pd(NH3)3(H2O)2+ and Pd(NH3)(H2O)32+. With standing, subsequent reactions ultimately produce a solution containing predominantly cis -Pd(NH3)2(H2O)22+ in equilibrium with small amounts of the tri- and mono-ammine complexes, and free ammonia.


1982 ◽  
Vol 92 (3) ◽  
pp. 327-339 ◽  
Author(s):  
E. TERASAWA ◽  
J. NOONAN ◽  
W. E. BRIDSON

Although the anterior pituitary gland has been shown to be a site of oestrogen feedback in the non-human primate, the role of the hypothalamus as a site of ovarian steroid feedback in facilitating gonadotrophin release has not been ruled out. In the present study, LH release in response to 2·5 mg progesterone with oestradiol benzoate (OB; 10 μg or 30 μg) 30 h earlier was observed in the ovariectomized monkey. Then pentobarbitone sodium was administered to block the progesterone-induced LH response. Serum levels of LH, oestradiol (OE2) and progesterone were measured by radioimmunoassay. In the first series of experiments a group of nine rhesus monkeys received subcutaneous implants of a small silicone elastomer capsule containing OE2. Two weeks later, either OB and oil, or OB and progesterone were injected sequentially. Oestradiol benzoate (10 μg) followed by oil 30 h later failed to cause any clear LH release, while 30 μg OB followed by oil induced a single peak of LH release with a peak latency of 16·5 ± 1·9 (s.e.m.) h after oil, and a duration of 69·8 ± 10·2 h. Regardless of the dose of OB, however, progesterone induced an LH release with two peaks in all animals. The peak latency (7·3 ±0·9 h) and the duration (19·3 ±1·3 h) of the first response with 30 μg OB + progesterone were virtually identical to those with 10 μg OB + progesterone (7·0 ±0·7 h, 18·0 ± 1·4 h respectively), whilst both components of the first response with 30 μg OB + progesterone were significantly shorter than those with 30 μg OB + oil (P < 0·001 for both). The peak latency of the second response with 30 μg OB + progesterone (42·7+ 4·8 h) was similar to that with 10 μg OB + progesterone (38·3 ±3·2 h), but the duration of the second response with 30 μg OB + progesterone (46·0 ± 1·7 h) was longer than that (35·7 ±3·2 h) with 10 μg OB + progesterone (P <0·02). In the second series of experiments the same nine animals received an OE2-capsule implantation and 10 μg OB (subthreshold) injections before pentobarbitone and progesterone. Pentobarbitone was first given 6 h before progesterone and additional injections were made to maintain the anaesthetized state for 21·6 ± 1·3 h. This period was to cover the progesterone-induced first LH response. Pentobarbitone completely blocked the expected first response of the progesterone-induced LH release in six animals. In the remaining three animals an enhanced LH surge occurred, but it consisted of a single peak with long latency 16·0 ± 2·0 h) and duration (66·0 ± 10·5 h) and was essentially the same as that observed in animals treated with a suprathreshold dose (30 μg) of OB alone. Anaesthesia did not, on the other hand, alter the response of the pituitary gland to LH releasing hormone. Therefore it was concluded that (1) sequential administration of oestrogen and progesterone induces an LH release with two phases in the ovariectomized monkey and (2) the facilitatory action of progesterone on the first phase of LH release requires the involvement of the brain.


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