Каждая латеральная полоса является ядром положительного ортогонально аддитивного оператора

{In this paper we continue a study of relationships between the lateral partial order $\sqsubseteq$ in a vector lattice (the relation $x \sqsubseteq y$ means that $x$ is a fragment of $y$) and the theory of orthogonally additive operators on vector lattices. It was shown in~\cite{pMPP} that the concepts of lateral ideal and lateral band play the same important role in the theory of orthogonally additive operators as ideals and bands play in the theory for linear operators in vector lattices. We show that, for a vector lattice $E$ and a lateral band $G$ of~$E$, there exists a vector lattice~$F$ and a positive, disjointness preserving orthogonally additive operator $T \colon E \to F$ such that ${\rm ker} \, T = G$. As a consequence, we partially resolve the following open problem suggested in \cite{pMPP}: Are there a vector lattice~$E$ and a lateral ideal in $E$ which is not equal to the kernel of any positive orthogonally additive operator $T\colon E\to F$ for any vector lattice $F$?

Projection lateral bands and lateral retracts

A projection lateral band $G$ in a Riesz space $E$ is defined to be a lateral band which is the image of an orthogonally additive projection $Q: E \to E$ possessing the property that $Q(x)$ is a fragment of $x$ for all $x \in E$, called a lateral retraction of $E$ onto $G$ (which is then proved to be unique). We investigate properties of lateral retracts, that are, images of lateral retractions, and describe lateral retractions onto principal projection lateral bands (i.e. lateral bands generated by single elements) in a Riesz space with the principal projection property. Moreover, we prove that every lateral retract is a lateral band, and every lateral band in a Dedekind complete Riesz space is a projection lateral band.

Pin Insertion to the Interosseous Hood Minimize the Finger Motion Restriction for the Proximal Phalangeal Percutaneous Fixation: A Cadaveric Study

Background: The purpose of this study was to identify the optimal pin insertion point to minimize finger motion restriction for proximal phalangeal fixation in cadaver models. Methods: We used 16 fingers from three fresh-frozen cadavers (age, 82–86 years). Each finger was dissected at the level of the carpometacarpal joint and fixated to a custom-built range of motion (ROM)-measuring apparatus after skin removal. The pin was inserted into the bone through four gliding soft tissues: the interosseous hood, dorsal capsule, lateral band, and sagittal band. Then, each tendon was pulled by a prescribed weight in three finger positions (flexion, extension, and intrinsic plus position). Changes in the metacarpophalangeal (MCP), proximal interphalangeal (PIP), and distal interphalangeal (DIP) angles were measured before and after pinning. We compared the differences between the insertion points using the Tukey-Kramer post hoc test. Results: Placement of pins into the sagittal band significantly restricted MCP joint flexion, while placement into the dorsal capsule and lateral band significantly restricted PIP joint flexion. Only placement into the interosseous hood showed no significant difference in joint angles between the three finger positions compared to pre-pin insertion. There were no significant effects on MCP, PIP, and DIP joint extension. Conclusions: The ROM of the MCP joint was obstructed due to pinning in most areas of insertion. However, pin insertion to the interosseous hood did not obstruct the finger flexion ROM compared to that of other gliding soft tissues; therefore, we believe that the interosseous hood may be a suitable pin insertion point for proximal phalangeal fixation.

Difference analysis of long drive swing mechanical movement towards ball velocity based on analysis kinematics approach between skill and unskill golf player

Tujuan penelitian ini adalah ingin mengetahui perbedaan long drive swing mechanical movement terhadap ball velocity berbasis pendekatan kinematics analysis antara skill dan unskill golf player. Adapun Analisis kinematik terdiri dari: trunk forword tilt, club stick velocity, knee flexion, wrist hinge at the top, leading arm angle, lateral band, hip rotation dan shoulder rotation. Metode yang digunakan dalam penelitian ini adalah metode deskriptif kuantitatif, sedangkan teknik analisis data menggunakan analisis uji perbedaan rata-rata. Sampel dalam penelitian ini adalah 2 atlet professional dan 4 atlet amatir di lingkungan Universitas Pendidikan Indonesia UPI Bandung, dengan rata-rata Tinggi Badan 1.63 ± 2.4 m, Berat Badan 72.4 ± 3.6 kg dan Usia 37.4 ± 7.6 tahun. Hasil penelitian ini menunjukan bahwa dari sepuluh variabel kinematika yang dianalisis terdapat empat indikator yang menunjukan hasil perbedaan signfikan pada taraf alpha 0.05 antara lain club speed at impact (t =0.007), lateral band after impact ball (t = 0.006), shoulder rotation (t = 0.005) dan flexion at elbow joint arm non dominant (t = 0.003).

Anatomical Basis for Arthroscopy of the Proximal Interphalangeal Joints

Background: Arthroscopy is a widely used minimally invasive technique. Nevertheless, no report describes the arthroscopic anatomy of the proximal interphalangeal (PIP) joint for portal creation. To facilitate arthroscopy, this study elucidated the anatomy of the lateral bands of the extensor mechanism and collateral ligaments of PIP joints. Methods: A total of 39 fingers from the right hands of 10 cadavers (4 males, 6 females) were evaluated in this study. We defined the extension line from the proximal interphalangeal volar crease as the C-line. We also defined an imaginary line along the distal edge of the proximal phalanx, which is parallel to the C-line, as the J-line. The distance between J-line and C-line was measured. On the C-line and J-line, we measured the following: from the dorsal skin to the lateral edge of the lateral band (LB), the dorsal edge of the collateral ligament (CL) and from the lateral band and the collateral ligament (D), the width of the finger (W). The finger half-width (M) was measured on the J-line. Comparison between the digits and comparison between radial and ulnar distance were measured and statistical analysis was performed. Results: All PIP joint spaces were distal from the C-line, except for one ring finger. The average distances between the J-line and C-line were 1.8–3.2 mm. On the C-line, only 11 cases (14.1%) showed an interval between the lateral bands and the collateral ligaments, but, on the J-line 72, cases (92.3%) had such an interval. The interval was located 1.6–2.9 mm in a dorsal direction from the midlateral on the J-line. Conclusions: Portal creation at the J-line is safer than at the C-line. This study revealed that safe portals for arthroscopy of the PIP joint are 2 mm dorsal to the midlateral line of the finger on the J-line.