Some identities involving the k-th power complements

The main purpose of this paper is using the elementary method to study the calculating problem of one kind infinite series involving the k-th power complements, and obtain several interesting identities

2-(4-Bromo­phen­yl)-3,4-dihydro­isoquinolin-2-ium thio­cyanate hemihydrate

In the title hemihydrated salt, C15H13BrN+·NCS−·0.5H2O, the two benzene rings are aligned at a dihedral angle of 46.9 (1)°. The six-membered heterocycle of the dihydro­isoquinoline unit adopts a half-chair conformation. The water mol­ecule and thio­cyanate ion are linked by O—H⋯N hydrogen bonds, generating a four-membered ring motif. In addition, C—H⋯O and C—H⋯S inter­actions link the components into a chain along the c axis. π–π inter­actions [centroid–centroid distance = 3.974 (2) Å] link the chains into sheets and further π—π [centroid–centroid distance = 3.746 (2) Å] and C—H⋯π inter­actions give rise to a three-dimensional nework

2-(4-Iodo­phen­yl)-1,2,3,4-tetra­hydro­isoquinoline-1-carbonitrile

In the title compound, C16H13IN2, the benzene ring of the tetra­hydro­isoquinoline moiety makes a dihedral angle of 45.02 (9)° with the benzene ring of the 4-iodo­phenyl fragment. The N atom and the adjacent unsubstituted C atom of the tetra­hydro­isoquinoline unit are displaced by 0.294 (2) and 0.441 (3) Å, respectively, from the plane through the remaining eight C atoms. In the crystal, pairs of adjacent mol­ecules are linked into dimers by weak inter­molecular C—H⋯π inter­actions

GEmo-CLAP: Gender-Attribute-Enhanced Contrastive Language-Audio Pretraining for Speech Emotion Recognition

Contrastive learning based pretraining methods have recently exhibited impressive success in diverse fields. In this paper, we propose GEmo-CLAP, a kind of efficient gender-attribute-enhanced contrastive language-audio pretraining (CLAP) model for speech emotion recognition. To be specific, we first build an effective emotion CLAP model Emo-CLAP for emotion recognition, utilizing various self-supervised learning based pre-trained models. Then, considering the importance of the gender attribute in speech emotion modeling, two GEmo-CLAP approaches are further proposed to integrate the emotion and gender information of speech signals, forming more reasonable objectives. Extensive experiments on the IEMOCAP corpus demonstrate that our proposed two GEmo-CLAP approaches consistently outperform the baseline Emo-CLAP with different pre-trained models, while also achieving superior recognition performance compared with other state-of-the-art methods.Comment: 5 page

2-(2-Hy­droxy­phen­yl)-3,4-dihydro­iso­quinolin-1(2H)-one

There are two independent mol­ecules in the asymmetric unit of the title compound, C15H13NO2, in both the six-membered dihydro­pyridine rings adopt a half-chair conformation. The two benzene rings make dihedral angles of 43.66 (10) and 62.22 (10)° in the two mol­ecules. In the crystal, the two independent mol­ecules are linked alternately by inter­molecular O—H⋯O hydrogen bonds, forming a zigzag chain along the c axis. Furthermore, inter­molecular C—H⋯π inter­actions link the chains into a three-dimensional network

4,4′,6,6′-Tetra­methyl-2,2′-bipyrimidine hexa­hydrate

In the title compound, C12H14N4·6H2O, the two pyrimidine rings make a dihedral angle of 5.285 (6)°. Inter­molecular O—H⋯O hydrogen bonds link the six water mol­ecules, generating edge-fused four-, five- or six-membered ring motifs and forming two-dimensional sheets. The sheets are stabilized by the formation of O—H⋯N hydrogen bonds between the water mol­ecules and the bipyrimidine mol­ecules, resulting in a three-dimensional network

2-(2-Iodo­phen­yl)-1,2,3,4-tetra­hydro­isoquinoline-1-carbonitrile

In the title compound, C16H13IN2, the two benzene rings make a dihedral angle of 67.26 (5)°. The six-membered heterocycle of the tetra­hydro­isoquinoline unit adopts a half-chair conformation. In the crystal, adjacent mol­ecules are linked by pairs of weak inter­molecular C—H⋯N hydrogen bonds, forming inversion dimers. An intra­molecular C—H⋯I close contact is also observed