Proof. Suppose that U1, . . . , Um are invariant subspaces of T ∈ L(V ). We wish to show that U1 + · · ·+ Um is also an invariant subspace. Consider any ~v ∈ U1 + · · ·+ Um. By definition, we can write ~v = ~u1 + · · ·+ ~um, for some ~u1 ∈ U1, . . . , ~um ∈ Um. Since U1, . . . , Um are invariant subspaces, by definition, we know T~u1 ∈ U1 ⊂ U1 + · · ·+ Um, ..., T~um ∈ Um ⊂ U1 + · · ·+ Um. Hence...

Water having entered a stream channel from the surrounding catchment may continue to have connections with the catchment. In the stream’s hyporheic zone, water “in the channel” exchanges with “groundwater” in the bed of the stream. Hyporheic exchange flows typically occur at scales small relative to the length and volumetric transport characteristics of the stream. Nevertheless, it is well docu...

Visual-vestibular and postural interactions can act as cues that trigger motion sickness and can also have a role in some anxiety disorders. We explore a method to detect individual sensitivity to visual-vestibular unusual patterns, which can signal a vulnerability to develop motion sickness and possibly anxiety disorders such as a fear of heights and panic. 65 undergraduate students were recru...

In the last few years in Malaysia, dengue fever has increased dramatically and has caused huge public health concerns. The present study aimed to establish a spatial distribution of dengue cases in the city of Kuala Lumpur using a combination of Geographic Information System (GIS) and spatial statistical tools. Collation of data from 1,618 dengue cases in 2009 was obtained from Kuala Lumpur Cit...

The creation of a surface breaks the translational symmetry of the bulk with the electrons redistributing to lower their energy, resulting in a new lattice structure. Surface relaxation and reconstruction have been studied for years, and it is generally assumed that theory and experiment are in fairly good agreement for the ground state properties at a metal surface. There is a conceptual pictu...

Gangguan pada sistem tenaga listrik bisa menimbulkan bahaya bukan hanya untuk peralatan tetapi juga manusia yang bekerja didekatnya. dapat muncul mulai dari konslet menyebabkan percikan api, hingga hubung singkat busur api. Tingkat api diperkirakan menentukan Personal Protective Equipment (PPE) harus digunakan oleh jika di daerah beraliran listrik. Selain level PPE, nilai arus jarak aman antara...

Pemanfaatan energi surya sebagai sumber listrik telah dilakukan dalam berbagai penelitian yang menjangkau macam sektor di antaranya rumah tangga, peternakan, pertanian, industri, dan infrastruktur fasilitas umum. Dalam ini akan memanfaatkan terbarukan yaitu matahari pengendalian kecepatan motor induksi tiga fasa. Energi dihasilkan dari panel disimpan pada baterai untuk menjadi inverter Tujuan a...